Class 12 Physics

Chapter 10 Solutions — Wave Optics

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Solutions

Overview

Step-by-step NCERT solutions for Wave Optics (Chapter 10, CBSE Class 12 Physics) — every question and answer worked out in full, not just the final result. You can also read the Wave Optics textbook chapter.

Solved

What these solutions cover

All 6 questions in Wave Optics are solved in the PDF. Here's what's inside, exercise by exercise:

Exercises

1.
Monochromatic light of wavelength 589 nm is incident from air on a water surface. What are the wavelength, frequency and speed of
- (a) reflected, and
- (b) refracted light? Refractive index of water is 1.33.
2.
What is the shape of the wavefront in each of the following cases:
- (a) Light diverging from a point source.
- (b) Light emerging out of a convex lens when a point source is placed at its focus.
- (c) The portion of the wavefront of light from a distant star intercepted by the Earth.
The refractive index of glass is 1.5. What is the speed of light in glass? (Speed of light in vacuum is 3.0 × 10⁸ m s⁻¹) (b) Is the speed of light in glass independent of the colour of light? If not, which of the two colours red and violet travels slower in a glass prism?
In a Young's double-slit experiment, the slits are separated by 0.28 mm and the screen is placed 1.4 m away. The distance between the central bright fringe and the fourth bright fringe is measured to be 1.2 cm. Determine the wavelength of light used in the experiment.
In Young's double-slit experiment using monochromatic light of wavelength lambda, the intensity of light at a point on the screen where path difference is lambda, is K units. What is the intensity of light at a point where path difference is lambda/3?
6.
A beam of light consisting of two wavelengths, 650 nm and 520 nm, is used to obtain interference fringes in a Young's double-slit experiment.
- (a) Find the distance of the third bright fringe on the screen from the central maximum for wavelength 650 nm.
- (b) What is the least distance from the central maximum where the bright fringes due to both the wavelengths coincide?

Sample

Worked examples

3 questions from Wave Optics, solved step by step.

Exercises

Monochromatic light of wavelength 589 nm is incident from air on a water surface. What are the wavelength, frequency and speed of (a) reflected, and (b) refracted light? Refractive index of water is 1.33.

Given: lambda_incident = 589 nm = 589 × 10⁻⁹ m, n_water = 1.33

Speed of light in air (vacuum): c = 3.0 × 10⁸ m/s

(a) Reflected light — remains in the same medium (air):

Reflection does not change the medium. Wavelength, frequency and speed are all unchanged.

Wavelength: lambda = 589 nm

Frequency: f = c / lambda = (3.0 × 10⁸) / (589 × 10⁻⁹) = 5.09 × 10¹⁴ Hz

Speed: v = 3.0 × 10⁸ m/s

(b) Refracted light — enters water (n = 1.33):

Frequency does not change on refraction (boundary condition): f = 5.09 × 10¹⁴ Hz

Speed in water: v = c / n = (3.0 × 10⁸) / 1.33 = 2.26 × 10⁸ m/s

Wavelength in water: lambda_w = v / f = lambda_air / n = 589 / 1.33 = 443 nm

Answer: (a) Reflected: lambda = 589 nm, f = 5.09 × 10¹⁴ Hz, v = 3.0 × 10⁸ m/s. (b) Refracted: lambda = 443 nm, f = 5.09 × 10¹⁴ Hz, v = 2.26 × 10⁸ m/s

Exercises

The refractive index of glass is 1.5. What is the speed of light in glass? (Speed of light in vacuum is 3.0 × 10⁸ m s⁻¹) (b) Is the speed of light in glass independent of the colour of light? If not, which of the two colours red and violet travels slower in a glass prism?

(a) Given: n_glass = 1.5, c = 3.0 × 10⁸ m/s

Speed of light in glass:

v = c / n = (3.0 × 10⁸) / 1.5 = 2.0 × 10⁸ m/s

(b) No, the speed of light in glass is NOT independent of colour.

The refractive index of glass varies with wavelength — this is called dispersion.

Violet light has a shorter wavelength than red light. Glass has a higher refractive index for violet than for red (n_violet > n_red).

Since v = c/n, a higher refractive index means lower speed.

Therefore, violet light travels slower than red light in a glass prism.

Answer: (a) v = 2.0 × 10⁸ m/s. (b) No; violet light travels slower than red light in glass (n_violet > n_red ⇒ v_violet < v_red).

Exercises

In a Young's double-slit experiment, the slits are separated by 0.28 mm and the screen is placed 1.4 m away. The distance between the central bright fringe and the fourth bright fringe is measured to be 1.2 cm. Determine the wavelength of light used in the experiment.

Given: d = 0.28 mm = 0.28 × 10⁻³ m, D = 1.4 m

Distance from central fringe to 4th bright fringe: x₄ = 1.2 cm = 1.2 × 10⁻² m

Position of nth bright fringe: xₙ = n × lambda × D / d

For n = 4: x₄ = 4 × lambda × D / d

Solving for lambda:

lambda = x₄ × d / (4 × D)

lambda = (1.2 × 10⁻² × 0.28 × 10⁻³) / (4 × 1.4)

lambda = (3.36 × 10⁻⁶) / 5.6

lambda = 6.0 × 10⁻⁷ m = 600 nm

Answer: lambda = 600 nm

All 6 questions in Wave Optics are solved step by step in the Solutions PDF above.

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Chapter 10 Solutions — Wave Optics

Overview

What these solutions cover

Exercises

Worked examples

Monochromatic light of wavelength 589 nm is incident from air on a water surface. What are the wavelength, frequency and speed of (a) reflected, and (b) refracted light? Refractive index of water is 1.33.

The refractive index of glass is 1.5. What is the speed of light in glass? (Speed of light in vacuum is 3.0 × 10⁸ m s⁻¹) (b) Is the speed of light in glass independent of the colour of light? If not, which of the two colours red and violet travels slower in a glass prism?

In a Young's double-slit experiment, the slits are separated by 0.28 mm and the screen is placed 1.4 m away. The distance between the central bright fringe and the fourth bright fringe is measured to be 1.2 cm. Determine the wavelength of light used in the experiment.

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