3. how many wavelengths of monochromatic light with an oscillation frequency v=5 * 10 ' 4 GP will fit on a path length of /-1.2 mm: 1) in a vacuum, 2) in glass? (refractive index of glass n=1.5
Answers
Answer:
Given:
λair = 589nm = 589 x 10-9 m
Speed of light in air, c = 3 × 108 m/s
Refractive index of water μ = 1.33
The ray will reflect back in the same medium as that of incident ray.
Hence, the wavelength, speed, and frequency of the reflected ray will be the same as that of the incident ray.
Frequency of light is given by the relation,
ν = (c/λ)
= (3 x 108)/ (589 x 10-9)
= (5.09 x 1014) Hz
Hence, the speed, frequency, and wavelength of the reflected light are
× 108 m/s), (5.09 ×1014 Hz), and (589 nm) respectively.
Frequency of light does not depend on the property of the medium in which it is travelling. Hence, the frequency of the refracted ray in water will be equal to the frequency of the incident or reflected light in air.
Therefore, Refracted frequency, ν = 5.09 ×1014 Hz
Speed of light in water is related to the refractive index of water as:
ν = (c/ μ)
= (3 x108)/ (1.33)
= (2.26 x 108) m/s
Wavelength of light in water is given by the relation,
λ = (ν/v)
= (2.26 x 108)/ (5.09 x 1014)
=444.007 x 10-9 m
= 444.01 m
Hence, the speed, frequency, and wavelength of refracted light are:
(2.26 ×108 m/s), (444.01nm), and (5.09 × 1014) Hz respectively
Question2.
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.
Answer:
The shape of the wavefront in case of a light diverging from a point source is spherical. The wavefront is shown in the figure:
Physics Class 12 Wave Optics Spherical Wavefront
The shape of the wavefront in case of a light emerging out of a convex lens when a point source is placed at its focus is a parallel grid.
Physics Class 12 Wave Optics Plane Wave
The portion of the wavefront of light from a distant star intercepted by the Earth is a plane.
Question 3.
(a) 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?
Answer:
Given:
Refractive index of glass, μ = 1.5
Speed of light, c = 3 × 108 m/s
Speed of light in glass is given by the relation,
Hence, the speed of light in glass is 2 × 108 m/s.
The speed of light in glass is not independent of the colour of light.
The refractive index of a violet component of white light is greater than the refractive index of a red component.