Advertisements
Advertisements
Question
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
Solution
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
RELATED QUESTIONS
Draw the sketches to differentiate between plane wavefront and spherical wavefront.
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 equation of a light wave is written as \[y = A \sin\left( kx - \omega t \right).\] Here, `y` represents _______ .
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 \[\lambda_a and \lambda_f,\]
Which of the following properties of light conclusively support the wave theory of light?
(a) Light obeys the laws of reflection.
(b) Speed of light in water is smaller than its speed in vacuum.
(c) Light shows interference.
(d) Light shows photoelectric effect.
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
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 white light is incident normally on a water film 1.0 × 10−4 cm thick. Find the wavelengths in the visible range (400 nm − 700 nm) which are strongly transmitted by the film. Refractive index of water = 1.33.
The optical path of a ray of light of a given wavelength travelling a distance of 3 cm in flint glass having refractive index 1.6 is the same as that on travelling a distance x cm through a medium having a refractive index 1.25. Determine the value of x.
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?
In Young’s double-slit experiment, the two coherent sources have different intensities. If the ratio of the maximum intensity to the minimum intensity in the interference pattern produced is 25:1, what is the ratio of the intensities of the two sources?
White light consists of wavelengths from 400 nm to 700 nm. What will be the wavelength range seen when white light is passed through a glass of refractive index 1.55?
A parallel beam of green light of wavelength 550 nm passes through a slit of width 0.4 mm. The intensity pattern of the transmitted light is seen on a screen that is 40 cm away. What is the distance between the two first-order minima?
Which of the following cannot produce two coherent sources?
State any four conditions for obtaining well defined and steady interference patterns.
A ray is an imaginary line ______.
Light appears to travel in straight lines since
State the theories which were proposed to explain nature of light.
