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
Draw the sketches to differentiate between plane wavefront and spherical wavefront.
Define a wavefront.
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?
When light propagates in vacuum, there is an electric field as well as a magnetic field. These fields ____________ .
(a) are constant in time
(b) have zero average value
(c) are perpendicular to the direction of propagation of light.
(d) are mutually perpendicular
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) \[\nu_B = \frac{1}{2}\left( \nu_A + \nu_C \right)\]
Find the range of frequency of light that is visible to an average human being
\[\left( 400\text{ nm }< \lambda < 700\text{ nm}\right)\]
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.
Find the thickness of a plate which will produce a change in optical path equal to half the wavelength λ of the light passing through it normally. The refractive index of the plate is μ.
Plane microwaves are incident on a long slit of width 5.0 cm. Calculate the wavelength of the microwaves if the first diffraction minimum is formed at θ = 30°.
Answer in brief:
The distance between two consecutive bright fringes in a biprism experiment using the light of wavelength 6000 Å is 0.32 mm by how much will the distance change if light of wavelength 4800 Å is used?
When light travels from an optically rarer medium to an optically denser medium, the speed decreases because of change in ______
Which of the following cannot produce two coherent sources?
What is the relation between phase difference and Optical path in terms of speed of light in a vacuum?
A Plane Wavefront of light of wavelength 5500 A.U. is incident on two slits in a screen perpendicular to the direction of light rays. If the total separation of 10 bright fringes on a screen 2 m away is 2 cm. Find the distance between the slits.
State any four conditions for obtaining well–defined and Steady interference patterns.
Two vectors of the same magnitude have a resultant equal to either of the two vectors. The angle between two vectors is
Light behaves as _________.
Light appears to travel in straight lines since
Light emerges out of a convex lens when a source of light kept at its focus. The shape of wavefront of the light is ______.
