Physics Class 12 NCERT Solutions: Chapter 10 Wave Optics Part 3

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Fresnel Number

Fresnel Number

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Q: 7. In a double-slit experiment the angular width of a fringe is found to be on a screen placed 1 m away. The wavelength of light used is. What will be the angular width of the fringe if the entire experimental apparatus is immersed in water? Take refractive index of water to be .

Answer:

Distance of the screen from the slits,

Wavelength of light used,

Angular width of the fringe in air,

Angular width of the fringe in water

Refractive index of water,

Refractive index is related to angular width as:

Therefore, the angular width of the fringe in water will reduce to.

Q: 8. What is the Brewster angle for air to glass transition? (Refractive index of glass.)

Answer:

Refractive index of glass,

Brewster angle

Brewster angle is related to refractive index as:

Therefore, the Brewster angle for air to glass transition is.

Q: 9. Light of wavelength falls on a plane reflecting surface. What are the wavelength and frequency of the reflected light? For what angle of incidence is the reflected ray normal to the incident ray?

Answer:

Wavelength of incident light,

Speed of light,

Frequency of incident light is given by the relation,

The wavelength and frequency of incident light is the same as that of reflected ray. Hence, the wavelength of reflected light is and its frequency is.

When reflected ray is normal to incident ray, the sum of the angle of incidence, and angle of reflection, is.

According to the law of reflection, the angle of incidence is always equal to the angle of reflection. Hence, we can write the sum as:

Therefore, the angle of incidence for the given condition is

Q: 10. Estimate the distance for which ray optics is good approximation for an aperture of and wavelength.

Answer:

Fresnel’s distance is the distance for which the ray optics is a good approximation. It is given by the relation,

Where,

Aperture width,

Wavelength of light,

Therefore, the distance for which the ray optics is a good approximation is.

Q: 11. The line emitted by hydrogen in a star is found to be red shifted by . Estimate the speed with which the star is receding from the Earth.

Answer:

Wavelength of line emitted by hydrogen,

.

Star’s red-shift,

Speed of light,

Let the velocity of the star receding away from the Earth be v.

The red shift is related with velocity as:

Therefore, the speed with which the star is receding away from the Earth is