Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
Wavelength of incident monochromatic light, λ = 589 nm = 589 × 10−9 m
Speed of light in air, c = 3 × 108 m/s
Refractive index of water, μ = 1.33
(a) The ray will reflect back in the same medium as that of the incident ray. Hence, the wavelength, speed, and frequency of the reflected ray will be the same as those of the incident ray.
Frequency of light is given by the relation,
v = `c/lambda`
= `(3 xx10^8)/(589 xx 10^(-9))`
= 5.09 × 1014 Hz
Hence, the speed, frequency, and wavelength of the reflected light are 3 × 108 m/s, 5.09 × 1014 Hz, and 589 nm, respectively.
(b) 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 the air.
∴ Refracted frequency, v = 5.09 ×1014 Hz
Speed of light in water is related to the refractive index of water as:
v = `c/μ`
= `(3 xx 10^8)/1.33`
= 2.26 × 108 m/s
Wavelength of light in water is given by the relation,
`lambda = v/v`
= `(2.26 xx 10^8)/(5.09 xx 10^(14))`
= 444.007 × 10−9 m
= 444.01 nm
Hence, the speed, frequency, and wavelength of refracted light are 2.26 × 108 m/s, 444.01 nm, and 5.09 × 1014 Hz, respectively.
APPEARS IN
संबंधित प्रश्न
The wavelength of light in a medium is \[\lambda = \lambda_0 /\mu,\] where \[\lambda \] is the wavelength in vacuum. A beam of red light \[\left( \lambda_0 = 720\text{ nm} \right)\] enters water. The wavelength in water is \[\lambda = \lambda_0 /\mu = 540\text{ nm.}\] To a person under water, does this light appear green?
Is it necessary to have two waves of equal intensity to study interference pattern? Will there be an effect on clarity if the waves have unequal intensity?
The speed of light depends ____________ .
An amplitude modulated (AM) radio wave bends appreciably round the corners of a 1 m × 1 m board but a frequency modulated (FM) wave only bends negligibly. If the average wavelengths of the AM and FM waves are \[\lambda_a and \lambda_f,\]
A light wave can travel
(a) in vacuum
(b) in vacuum only
(c) in a material medium
(d) in a material medium only
Three observers A, B and C measure the speed of light coming from a source to be νA, νBand νC. A moves towards the source and C moves away from the source at the same speed. B remains stationary. The surrounding space is vacuum everywhere.
(a) \[\nu_A > \nu_B > \nu_C\]
(b) \[\nu_A < \nu_B < \nu_C\]
(c) \[\nu_A = \nu_B = \nu_C\]
(d) \[\nu_B = \frac{1}{2}\left( \nu_A + \nu_C \right)\]
Three observers A, B and C measure the speed of light coming from a source to be νA, νBand νC. A moves towards the source and C moves away from the source at the same speed. B remains stationary. The surrounding space is water everywhere.
(a) \[\nu_A > \nu_B > \nu_C\]
(b) \[\nu_A < \nu_B < \nu_C\]
(c) \[\nu_A = \nu_B = \nu_C\]
(d) \[\nu_B = \frac{1}{2}\left( \nu_A + \nu_C \right)\]
The wavelength of sodium light in air is 589 nm. (a) Find its frequency in air. (b) Find its wavelength in water (refractive index = 1.33). (c) Find its frequency in water. (d) Find its speed in water.
The speed of yellow light in a certain liquid is 2.4 × 108 m s−1. Find the refractive index of the liquid.
Two narrow slits emitting light in phase are separated by a distance of 1⋅0 cm. The wavelength of the light is \[5 \cdot 0 \times {10}^{- 7} m.\] The interference pattern is observed on a screen placed at a distance of 1.0 m. (a) Find the separation between consecutive maxima. Can you expect to distinguish between these maxima? (b) Find the separation between the sources which will give a separation of 1.0 mm between consecutive maxima.
A parallel beam of light of wavelength 560 nm falls on a thin film of oil (refractive index = 1.4). What should be the minimum thickness of the film so that it strongly reflects the light?
Answer in brief:
In a double-slit arrangement, the slits are separated by a distance equal to 100 times the wavelength of the light passing through the slits.
- What is the angular separation in radians between the central maximum and an adjacent maximum?
- What is the distance between these maxima on a screen 50.0 cm from the slits?
The path difference between two waves meeting at a point is (11/4)λ. The phase difference between the two waves is ______
Two vectors of the same magnitude have a resultant equal to either of the two vectors. The angle between two vectors is
Light emerges out of a convex lens when a source of light kept at its focus. The shape of wavefront of the light is ______.
What did Thomas Young's interference experiment strongly support?
When is wave optics required?
How are the propagation and behaviour of light studied in wave optics?
Which set of topics is included in wave optics?
