Page No 385: - Chapter 10 Wave Optics Additional Exercise Solutions class 12 ncert solutions Physics - SaraNextGen [2024-2025]

Updated By SaraNextGen

On April 24, 2024, 11:35 AM

Question 10.18:

Two towers on top of two hills are 40 km apart. The line joining them passes 50 m above a hill halfway between the towers. What is the longest wavelength of radio waves, which can be sent between the towers without appreciable diffraction effects?

Answer:

Distance between the towers, d = 40 km

Height of the line joining the hills, d = 50 m.

Thus, the radial spread of the radio waves should not exceed 50 km.

Since the hill is located halfway between the towers, Fresnel’s distance can be obtained as:

ZP = 20 km = 2 × 10⁴ m

Aperture can be taken as:

a = d = 50 m

Fresnel’s distance is given by the relation,

Where,

λ = Wavelength of radio waves

Therefore, the wavelength of the radio waves is 12.5 cm.

Question 10.19:

A parallel beam of light of wavelength 500 nm falls on a narrow slit and the resulting diffraction pattern is observed on a screen 1 m away. It is observed that the first minimum is at a distance of 2.5 mm from the centre of the screen. Find the width of the slit.

Answer:

Wavelength of light beam, λ = 500 nm = 500 × 10⁻⁹ m

Distance of the screen from the slit, D = 1 m

For first minima, n = 1

Distance between the slits = d

Distance of the first minimum from the centre of the screen can be obtained as:

x = 2.5 mm = 2.5 × 10⁻³ m

It is related to the order of minima as:

Therefore, the width of the slits is 0.2 mm.

Question 10.20:

Answer the following Questions:

(a) When a low flying aircraft passes overhead, we sometimes notice

a slight shaking of the picture on our TV screen. Suggest a possible explanation.

(b) As you have learnt in the text, the principle of linear superposition of wave displacement is basic to understanding intensity distributions in diffraction and interference patterns. What is the justification of this principle?

Answer:

(a) Weak radar signals sent by a low flying aircraft can interfere with the TV signals received by the antenna. As a result, the TV signals may get distorted. Hence, when a low flying aircraft passes overhead, we sometimes notice a slight shaking of the picture on our TV screen.

(b) The principle of linear superposition of wave displacement is essential to our understanding of intensity distributions and interference patterns. This is because superposition follows from the linear character of a differential equation that governs wave motion. If y₁ and y₂ are the solutions of the second order wave equation, then any linear combination of y₁ and y₂ will also be the solution of the wave equation.

Question 10.21:

In deriving the single slit diffraction pattern, it was stated that the intensity is zero at angles of nλ/a. Justify this by suitably dividing the slit to bring out the cancellation.

Answer:

Consider that a single slit of width d is divided into n smaller slits.

Width of each slit, 

Angle of diffraction is given by the relation,

Now, each of these infinitesimally small slit sends zero intensity in directionθ. Hence, the combination of these slits will give zero intensity.