Lenses

What are Lenses?

Lenses are transparent optical devices made of glass or plastic that can bend (refract) light rays. Unlike plain glass sheets, lenses have curved surfaces that can converge or diverge light rays, making them essential components in various optical instruments like spectacles, cameras, telescopes, and microscopes.

Types of Lenses

Convex Lens (Converging Lens)

• Thicker in the middle and thinner at the edges
• Converges parallel light rays to a focal point
• Can form both real and virtual images
• Used in magnifying glasses, cameras, and human eyes

Concave Lens (Diverging Lens)

• Thinner in the middle and thicker at the edges
• Diverges parallel light rays away from a focal point
• Always forms virtual, erect, and diminished images
• Used in spectacles for myopia correction

Key Lens Terminology

Optical Center (O): The midpoint of the lens through which light passes without deviation

Centers of Curvature (C₁, C₂): Centers of the spheres from which the lens surfaces are formed

Optical Axis: Imaginary line passing through the centers of curvature and optical center

Principal Focus (F): Point where parallel rays converge (convex) or appear to diverge from (concave)

Focal Length (f): Distance from optical center to principal focus

Aperture: Effective area of the lens through which light passes

Image Formation Rules

Convex Lens Image Formation

• Object beyond 2F: Real, inverted, diminished image between F and 2F
• Object at 2F: Real, inverted, same size image at 2F
• Object between F and 2F: Real, inverted, magnified image beyond 2F
• Object at F: Image at infinity (no image formation)
• Object between F and lens: Virtual, erect, magnified image on same side

Concave Lens Image Formation

• Always forms virtual, erect, and diminished images
• Image position always between F and lens on object side

Mathematical Relationships

Lens Equation: 1/f = 1/v - 1/u

• f = focal length
• v = image distance
• u = object distance

Magnification: m = hi/ho = v/u

• hi = image height
• ho = object height
• Positive magnification = erect image
• Negative magnification = inverted image

Power of Lens: P = 1/f (in meters)

• SI unit: Dioptre (D)
• Positive power = convex lens
• Negative power = concave lens

Applications of Lenses

Compound Microscope

• Uses two convex lenses: objective (short focal length) and eyepiece (longer focal length)
• Produces highly magnified virtual images of small objects

Refracting Telescope

• Uses objective lens (large focal length, large aperture) and eyepiece (small focal length)
• Makes distant objects appear closer and clearer

Spectacles

• Convex lenses correct hypermetropia (far-sightedness)
• Concave lenses correct myopia (near-sightedness)

Question and Answer Study Material

Basic Concepts and Definitions

Q1: What is a lens and how does it differ from a plain glass sheet? A1: A lens is a transparent optical device with at least one curved surface that can refract light rays. Unlike a plain glass sheet that allows light to pass through without changing direction significantly, a lens has curved refracting surfaces that bend light rays. When sunlight passes through a glass sheet, the illuminated area remains the same size regardless of distance. However, a lens can focus light rays to a small point, concentrating the light energy enough to burn paper.

Q2: What are the two main types of lenses? Explain their characteristics. A2: The two main types of lenses are:

Convex Lens:

• Thicker in the middle and thinner at the edges
• Converges parallel light rays to a focal point
• Can form both real and virtual images
• Shows objects magnified when used as a magnifying glass
• Also called a converging lens

Concave Lens:

• Thinner in the middle and thicker at the edges
• Diverges parallel light rays away from a focal point
• Always forms virtual, erect, and diminished images
• Cannot be used to burn paper by focusing sunlight
• Also called a diverging lens

Q3: How can you distinguish between a convex and concave lens practically? A3: There are several practical methods:

Visual observation method:

• Look at the lens shape - convex is thicker in middle, concave is thinner in middle

Letter movement test:

• Hold the lens over printed text and move it sideways
• Through a convex lens, letters appear to move in the opposite direction
• Through a concave lens, letters appear to move in the same direction

Sunlight focusing test:

• Try to focus sunlight through the lens onto paper
• Convex lens can focus light and burn paper
• Concave lens cannot focus light to burn paper

Q4: Define the following terms related to lenses: optical center, centers of curvature, optical axis, and aperture. A4:

Optical Center (O): The midpoint of a lens through which light rays pass without deviation. It is the geometric center of the lens.

Centers of Curvature (C₁, C₂): Since each refracting surface of a lens is part of a sphere, the centers of these spheres are called centers of curvature. A lens has two centers of curvature.

Optical Axis: An imaginary straight line passing through both centers of curvature and the optical center of the lens. It represents the principal axis of the lens.

Aperture: The effective area or diameter of the lens through which light can pass. In optical instruments, the aperture can be controlled using stops to regulate the amount of light entering.

Principal Focus and Focal Length

Q5: What is the principal focus of a lens? How does it differ for convex and concave lenses? A5: The principal focus is a specific point on the optical axis related to parallel light rays.

For Convex Lens:

• When parallel light rays near the optical axis fall on a convex lens, they converge to a point on the optical axis after refraction
• This point of convergence is the principal focus (F)
• It is a real focus because light rays actually pass through this point
• A convex lens has two principal foci, one on each side, equidistant from the optical center

For Concave Lens:

• When parallel light rays fall on a concave lens, they diverge after refraction
• The point from which the diverged rays appear to come is the principal focus
• It is a virtual focus because light rays do not actually pass through this point
• A concave lens also has two principal foci on either side

Q6: What is focal length? How can you find the focal length of a convex lens practically? A6: Focal length (f) is the distance from the optical center of the lens to its principal focus.

To find focal length of a convex lens practically - Distant Object Method:

• Take the convex lens and a screen (white paper/wall)
• Point the lens toward a distant object like a tree or building
• Move the screen behind the lens until you get a clear, sharp image of the distant object
• Measure the distance between the lens and the screen using a ruler
• This distance is approximately equal to the focal length of the lens

This method works because rays from a distant object are nearly parallel, and they converge at the focal point after passing through the lens.

Q7: Explain the difference between real and virtual focus with examples. A7:

Real Focus:

• Light rays actually converge and pass through the focal point
• Found in convex lenses
• Can be obtained on a screen
• Example: The focal point of a convex lens where sunlight can be focused to burn paper

Virtual Focus:

• Light rays appear to diverge from the focal point, but don't actually pass through it
• Found in concave lenses
• Cannot be obtained on a screen
• Example: The focal point of a concave lens from which diverged rays appear to come

The key difference is that real focus involves actual convergence of light rays, while virtual focus involves apparent divergence.

Image Formation by Convex Lens

Q8: Describe image formation when an object is placed beyond 2F from a convex lens. A8: When an object is placed beyond 2F (twice the focal length) from a convex lens:

Position of image: Between F and 2F on the opposite side of the lens Characteristics of image:

• Real (can be obtained on screen)
• Inverted (upside down)
• Diminished (smaller than object)

Ray diagram construction:

• Draw a ray parallel to optical axis from object top - this ray passes through F after refraction
• Draw a ray through optical center - this ray continues straight
• Draw a ray through F toward lens - this ray becomes parallel to optical axis after refraction
• The intersection point of these rays gives the image position

Applications: This principle is used in cameras and human eyes to form images of distant objects.

Q9: What happens to the image when an object is placed between F and 2F of a convex lens? A9: When an object is placed between F and 2F of a convex lens:

Position of image: Beyond 2F on the opposite side of the lens Characteristics of image:

• Real (can be projected on screen)
• Inverted (upside down)
• Magnified (larger than object)

This is the principle used in:

• Projectors to display enlarged images on screens
• Slide projectors in presentations
• The objective lens of compound microscopes

The magnification is greater than 1, meaning the image is larger than the object.

Q10: Explain image formation when an object is placed between the focal point and optical center of a convex lens. A10: When an object is placed between F and the optical center of a convex lens:

Position of image: On the same side as the object Characteristics of image:

• Virtual (cannot be obtained on screen, can only be seen)
• Erect (same orientation as object)
• Magnified (larger than object)

Ray diagram explanation:

• Rays from the object diverge after passing through the lens
• These diverged rays appear to come from a point on the same side as the object
• The eye sees an enlarged, erect image when looking through the lens

Applications:

• Magnifying glass for reading small text
• Simple microscope for examining small objects
• Reading glasses for people with presbyopia

Q11: What happens when an object is placed exactly at the focal point of a convex lens? A11: When an object is placed exactly at the focal point (F) of a convex lens:

Image formation: No image is formed or the image is formed at infinity

Explanation:

• Light rays from the object become parallel to the optical axis after refraction
• Parallel rays never meet, so no image is formed at any finite distance
• Theoretically, the image is said to be formed at infinity

Ray diagram:

• All rays from the object emerge parallel to the optical axis
• Since parallel lines meet at infinity, the image is at infinity

Practical significance:

• This principle is used in searchlights and car headlights
• The light source is placed at the focal point to produce a parallel beam of light
• This creates maximum illumination over long distances

Image Formation by Concave Lens

Q12: Describe the image formation by a concave lens. What are the characteristics of images formed? A12: A concave lens always forms images with the same characteristics regardless of object position:

Position of image: Always between the focal point and the lens, on the same side as the object

Characteristics of image (always):

• Virtual (cannot be obtained on screen)
• Erect (same orientation as object)
• Diminished (smaller than object)

Why these characteristics remain constant:

• Concave lens diverges all incoming light rays
• Diverged rays cannot converge to form a real image
• The apparent convergence point (where rays seem to come from) is always on the object side
• The diverging nature ensures the image is always smaller than the object

Applications:

• Spectacles for correcting myopia (nearsightedness)
• Peepholes in doors for wide-angle viewing
• Vehicle side mirrors marked "objects are closer than they appear"

Q13: Why can't a concave lens form a real image? A13: A concave lens cannot form a real image because of its diverging nature:

Physical reason:

• Concave lens has a shape that causes light rays to spread out (diverge) after refraction
• For a real image to form, light rays must actually converge and meet at a point
• Since concave lens always diverges rays, they never actually meet

Geometric explanation:

• When parallel rays fall on a concave lens, they diverge after refraction
• The diverged rays appear to come from the focal point, but don't actually pass through it
• Real images require actual intersection of light rays, which never happens with concave lens

Comparison with convex lens:

• Convex lens can converge rays to form real images
• Concave lens can only create virtual images where rays appear to diverge from a point

This is why concave lenses are used for correction (spreading out light) rather than image projection.

Lens Formula and Magnification

Q14: State the lens formula and explain the sign convention used. A14:

Lens Formula: 1/f = 1/v - 1/u

Where:

• f = focal length of the lens
• v = distance of image from optical center
• u = distance of object from optical center

Alternative form: f = uv/(u + v)

Cartesian Sign Convention:

• All distances are measured from the optical center of the lens
• Distances in the direction of incident light are positive
• Distances opposite to incident light direction are negative
• Heights above optical axis are positive
• Heights below optical axis are negative

Practical application:

• Object distance (u) is always negative (opposite to incident light)
• For real images: v is positive (same direction as incident light)
• For virtual images: v is negative (opposite to incident light)
• For convex lens: f is positive
• For concave lens: f is negative

Q15: Define magnification and derive its formula. What does the sign of magnification indicate? A15:

Definition: Magnification is the ratio of the height of the image to the height of the object. It indicates how many times larger or smaller the image is compared to the object.

Formula: m = hi/ho = v/u

Where:

• m = magnification (no unit)
• hi = height of image
• ho = height of object
• v = image distance
• u = object distance

Sign significance:

• Positive magnification (+): Image is erect (virtual image)
• Negative magnification (-): Image is inverted (real image)

Magnitude significance:

• |m| > 1: Image is magnified (larger than object)
• |m| < 1: Image is diminished (smaller than object)
• |m| = 1: Image is same size as object

Examples:

• m = +2: Virtual, erect image, twice the object size
• m = -0.5: Real, inverted image, half the object size

Q16: Solve this problem: An object 4 cm high is placed 30 cm from a convex lens of focal length 20 cm. Find the image distance, magnification, and image characteristics. A16:

Given:

• Object height (ho) = +4 cm
• Object distance (u) = -30 cm (negative as per sign convention)
• Focal length (f) = +20 cm (positive for convex lens)

To find: Image distance (v), magnification (m), and image characteristics

Step 1: Find image distance using lens formula 1/f = 1/v - 1/u 1/20 = 1/v - 1/(-30) 1/20 = 1/v + 1/30 1/v = 1/20 - 1/30 = (3-2)/60 = 1/60 Therefore, v = +60 cm

Step 2: Calculate magnification m = v/u = 60/(-30) = -2

Step 3: Find image height hi = m × ho = (-2) × 4 = -8 cm

Results:

• Image distance: 60 cm from lens (opposite side)
• Magnification: -2
• Image height: 8 cm
• Image characteristics: Real, inverted, magnified (twice the object size)

The negative sign of magnification indicates the image is inverted and real.

Power of Lens

Q17: What is the power of a lens? How is it related to focal length? A17:

Definition: Power of a lens is its ability to converge or diverge light rays. It is the reciprocal of focal length when focal length is expressed in meters.

Formula: P = 1/f (where f is in meters)

SI Unit: Dioptre (D)

• 1 dioptre = 1 m⁻¹
• A lens with focal length 1 meter has power 1 dioptre

Relationship with focal length:

• Shorter focal length = Higher power
• Longer focal length = Lower power
• Convex lens = Positive power
• Concave lens = Negative power

Practical significance:

• High power lenses can bend light more effectively
• Eye specialists prescribe lens power in dioptres
• Camera lenses with high power can focus light better

Examples:

• f = 0.5 m, P = 1/0.5 = +2 D (convex lens)
• f = -0.25 m, P = 1/(-0.25) = -4 D (concave lens)

Q18: A concave lens has focal length 25 cm. Calculate its power and explain what the sign indicates. A18:

Given:

• Focal length of concave lens = 25 cm = 0.25 m
• For concave lens, focal length is negative = -0.25 m

Calculation: Power (P) = 1/f = 1/(-0.25) = -4 D

Result: Power = -4 dioptres

Sign significance:

• Negative power indicates it is a concave lens
• Negative sign shows the lens has diverging nature
• The lens spreads out light rays instead of converging them

Practical application:

• This lens would be prescribed for myopia (nearsightedness)
• The prescription would show -4.0 D
• Such lenses help diverge light rays before they enter the eye
• This compensates for the eye's excessive converging power in myopia

Q19: Compare the power of two lenses: one with focal length 50 cm and another with focal length 20 cm. Which is more powerful? A19:

Lens 1:

• Focal length = 50 cm = 0.5 m
• Power = 1/f = 1/0.5 = +2 D

Lens 2:

• Focal length = 20 cm = 0.2 m
• Power = 1/f = 1/0.2 = +5 D

Comparison:

• Lens 1 power: +2 D
• Lens 2 power: +5 D
• Lens 2 is more powerful than Lens 1

Explanation:

• Higher power means greater ability to bend light rays
• Shorter focal length results in higher power
• Lens with 20 cm focal length can converge light more effectively
• This principle is used in optical instruments where strong convergence is needed

Applications:

• High power lenses are used in microscope objectives
• Camera lenses with high power provide better magnification
• Reading glasses for elderly people often have high positive power

Optical Instruments

Q20: Explain the working principle of a compound microscope. What are the characteristics of the lenses used? A20:

Working Principle: A compound microscope uses two convex lenses to produce highly magnified images of small objects.

Components:

• Objective lens: Short focal length, placed close to object
• Eyepiece lens: Longer focal length, used for final observation

Step-by-step working:

1. Object is placed between F and 2F of the objective lens
2. Objective forms a real, inverted, magnified image beyond 2F
3. This image acts as object for the eyepiece
4. The image from objective falls between F and optical center of eyepiece
5. Eyepiece forms a virtual, erect, further magnified image
6. Final image is highly magnified but inverted with respect to original object

Lens Characteristics: Objective lens:

• Convex lens with short focal length
• Small aperture for better resolution
• High magnification capability

Eyepiece lens:

• Convex lens with longer focal length than objective
• Larger aperture for comfortable viewing
• Acts as magnifying glass for the image formed by objective

Why short focal length for objective?

• Shorter focal length provides higher magnification
• Better resolution of fine details
• More powerful convergence of light rays

Q21: How does a refracting telescope work? What are the lens specifications required? A21:

Working Principle: A refracting telescope uses two convex lenses to make distant objects appear closer and clearer.

Components:

• Objective lens: Large focal length, large aperture
• Eyepiece lens: Short focal length, small aperture

Step-by-step working:

1. Distant object sends nearly parallel light rays
2. Objective lens converges these rays to form a real, inverted, diminished image at its focal plane
3. This image is positioned between the focal point and optical center of the eyepiece
4. Eyepiece acts as a magnifying glass, forming a virtual, erect, magnified image of the objective's image
5. Final image appears larger and closer than the actual distant object

Lens Specifications:

Objective lens requirements:

• Long focal length for better image formation of distant objects
• Large aperture to collect maximum light from distant sources
• High optical quality for clear images

Eyepiece lens requirements:

• Short focal length for high magnification
• Smaller aperture adequate for eye viewing
• Good optical quality for comfortable observation

Telescope length calculation:

• Length ≈ Focal length of objective + Focal length of eyepiece
• This determines the physical size of the telescope

Q22: Why are different lens combinations used in microscopes and telescopes? A22:

The lens combinations are optimized for different purposes:

Compound Microscope: Purpose: Magnify small, nearby objects

Objective lens:

• Short focal length for high magnification
• Small aperture for good resolution
• Object placed close to lens

Eyepiece:

• Medium focal length
• Further magnifies the already magnified image
• Total magnification = Objective magnification × Eyepiece magnification

Refracting Telescope: Purpose: View distant objects clearly

Objective lens:

• Long focal length to handle parallel rays from distant objects
• Large aperture to collect maximum light
• Forms small, bright image of distant object

Eyepiece:

• Short focal length to magnify the small image formed by objective
• Makes distant objects appear closer and larger

Key Differences:

Light gathering:

• Microscope: Uses artificial light source, small aperture sufficient
• Telescope: Must collect faint light from distant stars, needs large aperture

Object distance:

• Microscope: Objects are very close (cm range)
• Telescope: Objects are very far (km to light-years)

Image requirements:

• Microscope: Maximum magnification of fine details
• Telescope: Brightness and clarity of distant objects

This is why the lens specifications are exactly opposite in these two instruments.

Q23: Explain how spectacles work to correct vision defects. A23:

Vision defects and their correction:

Myopia (Nearsightedness): Problem: Eye converges light too much, image forms before retina Correction: Concave lens diverges light before it enters the eye Lens specification: Negative power (diverging lens) Result: Light rays spread out, allowing proper focus on retina

Hypermetropia (Farsightedness): Problem: Eye converges light too little, image would form behind retina

Correction: Convex lens converges light before it enters the eye Lens specification: Positive power (converging lens) Result: Light rays converge more, bringing focus onto retina

How spectacles work:

• Spectacle lens modifies the light rays before they enter the eye
• This compensates for the eye's focusing defects
• The corrected rays then form a sharp image on the retina
• Brain interprets this as clear vision

Prescription interpretation:

• Positive power (+): Convex lens for hypermetropia
• Negative power (-): Concave lens for myopia
• Higher numerical value: More severe defect requiring stronger lens

Example: +2.0 D means convex lens with 0.5 m focal length for hypermetropia correction.

The spectacle lens essentially acts as a pre-processor, adjusting the light before the eye's natural lens system takes over.

Problem-Solving Practice

Q24: A convex lens forms a real image of the same size as the object. If the object is 40 cm from the lens, find the focal length. A24:

Given:

• Real image of same size as object (magnification = -1)
• Object distance (u) = -40 cm (negative by sign convention)
• Image is real and same size

Analysis: When magnification = -1 (negative indicates real, inverted image):

• |m| = 1 means image size = object size
• This happens when object is placed at 2F from the lens
• For same size image: object distance = image distance = 2f

Solution: Since object is at 2F: u = -2f Given: u = -40 cm Therefore: -40 = -2f Focal length: f = 20 cm

Verification using lens formula: At 2F, image also forms at 2F on opposite side So v = +40 cm

Using 1/f = 1/v - 1/u: 1/f = 1/40 - 1/(-40) = 1/40 + 1/40 = 2/40 = 1/20 Therefore: f = 20 cm

Answer: Focal length = 20 cm

Q25: An object is placed 15 cm from a concave lens of focal length 10 cm. Calculate the image distance and magnification. A25:

Given:

• Object distance (u) = -15 cm (negative by sign convention)
• Focal length (f) = -10 cm (negative for concave lens)

To find: Image distance (v) and magnification (m)

Step 1: Calculate image distance using lens formula 1/f = 1/v - 1/u 1/(-10) = 1/v - 1/(-15) -1/10 = 1/v + 1/15 1/v = -1/10 - 1/15 = (-3-2)/30 = -5/30 = -1/6 Therefore: v = -6 cm

Step 2: Calculate magnification m = v/u = (-6)/(-15) = +0.4

Results:

• Image distance: 6 cm from lens (same side as object due to negative sign)
• Magnification: +0.4

Image characteristics:

• Virtual (negative image distance)
• Erect (positive magnification)
• Diminished (magnification < 1)
• Image is 0.4 times the object height

This confirms the typical behavior of concave lenses always forming virtual, erect, and diminished images.

Advanced Applications

Q26: How would you design a simple telescope? What factors should be considered? A26:

Design Components Required:

Lenses:

• Objective lens: Convex lens with long focal length (50-100 cm) and large diameter (5-10 cm)
• Eyepiece lens: Convex lens with short focal length (2-5 cm) and small diameter

Structural Materials:

• Long tube (PVC pipe) with length = fo + fe (approximately)
• Lens holders and mounting system
• Adjustable eyepiece for focusing

Design Considerations:

Objective lens selection:

• Longer focal length gives better image quality for distant objects
• Larger aperture collects more light for brighter images
• Higher quality glass reduces aberrations

Eyepiece selection:

• Shorter focal length provides higher magnification
• Must be comfortable for eye viewing
• Quality affects final image sharpness

Tube length calculation:

• Minimum length = focal length of objective + focal length of eyepiece
• Allows for proper focusing adjustments
• Longer tube may be needed for focusing mechanism

Magnification calculation:

• Magnification = fo/fe (focal length of objective ÷ focal length of eyepiece)
• Higher magnification requires longer objective focal length or shorter eyepiece focal length

Practical tips:

• Start with moderate magnification (10-20x) for easier use
• Ensure stable mounting to reduce vibrations
• Consider portability vs. performance trade-offs

Q27: Compare the advantages and limitations of using lenses in optical instruments. A27:

Advantages of Lenses in Optical Instruments:

Image Formation Capabilities:

• Can form both real and virtual images as needed
• Provide controllable magnification
• Offer good image quality with proper design

Light Handling:

• Efficient light transmission through transparent materials
• Can be coated to reduce reflections and improve transmission
• Compact compared to mirror systems

Versatility:

• Single lens can serve multiple functions
• Can be combined for complex optical systems
• Easy to manufacture in various shapes and sizes

Cost-effectiveness:

• Relatively inexpensive to produce
• Durable with proper care
• Easy to replace if damaged

Limitations of Lenses in Optical Instruments:

Optical Aberrations:

• Chromatic aberration: Different colors focus at different points
• Spherical aberration: Rays from edge focus differently than central rays
• Distortion: Image shape changes, especially at edges

Material Limitations:

• Glass can break easily
• Limited temperature range for optimal performance
• Weight increases with size for large objectives

Light Loss:

• Some light lost due to reflection at surfaces
• Absorption in glass material
• Multiple lens systems increase light loss

Manufacturing Constraints:

• Difficult to make very large lenses without distortion
• Perfect spherical surfaces challenging to achieve
• Quality control affects performance significantly

Maintenance Issues:

• Surfaces can get dirty or scratched
• Require periodic cleaning and care
• Alignment can shift over time

Despite limitations, lenses remain fundamental in optics due to their versatility and effectiveness in most applications.

Key Points for Exam Preparation

Essential Formulas to Remember:

• Lens Formula: 1/f = 1/v - 1/u
• Magnification: m = hi/ho = v/u
• Power: P = 1/f (f in meters)

Sign Convention Rules:

• Object distance: Always negative
• Real image distance: Positive
• Virtual image distance: Negative
• Convex lens focal length: Positive
• Concave lens focal length: Negative

Image Characteristics by Object Position:

• Beyond 2F: Real, inverted, diminished
• At 2F: Real, inverted, same size
• Between F and 2F: Real, inverted, magnified
• At F: Image at infinity
• Between F and lens: Virtual, erect, magnified

Applications Summary:

• Convex lens: Cameras, projectors, magnifying glass, spectacles for hypermetropia
• Concave lens: Spectacles for myopia, peepholes, diverging applications
• Compound microscope: Two convex lenses for magnifying small objects
• Telescope: Two convex lenses for viewing distant objects

Common Exam Problem Types:

• Lens formula calculations
• Magnification problems
• Power calculations
• Ray diagram construction
• Image characteristic determination
• Optical instrument working principles