Chapter 9: Ray Optics and Optical Instruments Short Questions | physics Class 12 CBSE

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Chapter 9: Ray Optics and Optical Instruments Short Questions | physics Class 12 CBSE | ByteNotes.in

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Question 1

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State the two laws of reflection of light as applicable to spherical mirrors.

The angle of reflection equals the angle of incidence (angle between the reflected ray and the normal equals the angle between the incident ray and the normal).
The incident ray, the reflected ray, and the normal to the reflecting surface at the point of incidence all lie in the same plane.
These laws hold at every point on any reflecting surface, whether plane or curved, and the normal for a spherical mirror is along the radius joining the centre of curvature to the point of incidence.

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Question 2

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Derive the relation between focal length and radius of curvature for a spherical mirror.

For a ray parallel to the principal axis striking a concave mirror at M, the normal CM is perpendicular to the mirror. Using geometry, angle MCP = θ and angle MFP = 2θ.
For paraxial rays (small θ), tan θ ≈ θ, giving MD/FD = 2(MD/CD), so FD = CD/2.
Since D is close to P for paraxial rays, FD = f and CD = R, therefore f = R/2.

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Question 3

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State the Cartesian sign convention for measuring distances in mirror and lens systems.

All distances are measured from the pole of the mirror or the optical centre of the lens along the principal axis.
Distances measured in the same direction as the incident light are taken as positive; those measured in the opposite direction are negative.
Heights measured upwards above the principal axis are positive; heights measured downwards are negative.

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Question 4

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Define linear magnification for a spherical mirror and write its formula in terms of object and image distances.

Linear magnification m is defined as the ratio of the height of the image (h') to the height of the object (h): m = h'/h.
Using the sign convention and similar triangles in the mirror geometry, it can be shown that m = -v/u, where v is the image distance and u is the object distance.
A negative value of m indicates a real, inverted image, while a positive value indicates a virtual, erect image.

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Question 5

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State Snell's law of refraction and define the refractive index of a medium.

Snell's law states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is constant: sin i / sin r = n21.
The constant n21 is called the refractive index of the second medium with respect to the first medium; it is a characteristic of the pair of media and depends on the wavelength of light.
If n21 > 1, the refracted ray bends towards the normal (medium 2 is optically denser); if n21 < 1, it bends away (medium 2 is optically rarer).

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Question 6

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Explain why optical density should not be confused with mass density, giving an example.

Optical density is the ratio of the speed of light in two media and determines how much a medium bends light, while mass density is mass per unit volume.
It is possible that a medium with greater optical density has lower mass density than an optically rarer medium.
For example, turpentine has a lower mass density than water, but its optical density is higher than that of water.

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Question 7

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Define critical angle and state the condition for total internal reflection.

The critical angle ic is the angle of incidence in a denser medium for which the angle of refraction in the rarer medium is exactly 90°.
The mathematical condition is sin ic = n21, where n21 is the refractive index of the rarer medium with respect to the denser medium.
Total internal reflection occurs when (i) light travels from a denser to a rarer medium and (ii) the angle of incidence exceeds the critical angle; under these conditions, no refraction occurs and all light is reflected back.

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Question 8

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How do optical fibres work? State the physical principle behind them.

Optical fibres work on the principle of total internal reflection. Each fibre has a high-refractive-index core surrounded by a cladding of lower refractive index.
When light is directed into one end of the fibre at a suitable angle, it strikes the core-cladding interface at an angle greater than the critical angle and undergoes repeated total internal reflections along the length of the fibre.
Since there is no transmission of light at each reflection, there is no appreciable loss of intensity; the light signal travels to the other end even if the fibre is bent.

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Question 9

Quick Recall

Write the formula for refraction at a single spherical surface and identify each symbol.

The formula is n2/v - n1/u = (n2 - n1)/R, derived by applying Snell's law and small angle approximation to rays incident on the curved interface.
Here, n1 and n2 are the refractive indices of the first and second media respectively, u is the object distance, v is the image distance, and R is the radius of curvature of the spherical surface.
This relation holds for any curved spherical surface and is the starting point for deriving the lens maker's formula by applying it successively at both surfaces of a thin lens.

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Question 10

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Write the lens maker's formula and state when it is useful.

The lens maker's formula is 1/f = (n21 - 1)(1/R1 - 1/R2), where n21 is the refractive index of the lens material with respect to the surrounding medium, and R1, R2 are the radii of curvature of the two surfaces.
It is useful for designing lenses of desired focal length by choosing surfaces of appropriate radii of curvature.
The formula applies to both convex and concave lenses; for a concave lens, R1 is negative and R2 is positive, giving a negative f.

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Question 11

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Define power of a lens and state its SI unit. How does sign of power relate to lens type?

Power of a lens P is defined as the tangent of the angle by which it converges or diverges a beam of light parallel to the principal axis falling at unit distance from the optical centre; mathematically P = 1/f.
The SI unit of power is dioptre (D), where 1 D = 1 m⁻¹; a lens of focal length 1 metre has power of one dioptre.
Power is positive for a converging (convex) lens and negative for a diverging (concave) lens.

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Question 12

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State the formula for the effective focal length of two thin lenses in contact and explain the advantage of such a combination.

For two thin lenses of focal lengths f1 and f2 in contact, the combined focal length f satisfies 1/f = 1/f1 + 1/f2, and the equivalent power is P = P1 + P2.
Combination of lenses helps obtain converging or diverging lenses of desired magnification and enhances the sharpness of the image.
The total magnification of the combination is the product of individual magnifications: m = m1 × m2 × m3 ...

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Question 13

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What happens when a ray of light passes through a rectangular glass slab? Explain with reference to lateral shift.

When light enters a rectangular glass slab, refraction occurs at both the air-glass and glass-air interfaces; at the second interface r2 = i1, so the emergent ray is parallel to the incident ray.
Although there is no net deviation in direction, the emergent ray is laterally displaced with respect to the incident ray — this displacement is called lateral shift.
The lateral shift increases with the thickness of the slab and with the angle of incidence, and depends on the refractive index of the glass.

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Chapter 9: Ray Optics and Optical Instruments | Short Questions

State the two laws of reflection of light as applicable to spherical mirrors.

Derive the relation between focal length and radius of curvature for a spherical mirror.

State the Cartesian sign convention for measuring distances in mirror and lens systems.

Define linear magnification for a spherical mirror and write its formula in terms of object and image distances.

State Snell's law of refraction and define the refractive index of a medium.

Explain why optical density should not be confused with mass density, giving an example.

Define critical angle and state the condition for total internal reflection.

How do optical fibres work? State the physical principle behind them.

Write the formula for refraction at a single spherical surface and identify each symbol.

Write the lens maker's formula and state when it is useful.

Define power of a lens and state its SI unit. How does sign of power relate to lens type?

State the formula for the effective focal length of two thin lenses in contact and explain the advantage of such a combination.

What happens when a ray of light passes through a rectangular glass slab? Explain with reference to lateral shift.

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