Advertisements
Advertisements
Question
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.
Advertisements
Solution 1
Let dfg and dm m be the distances by the ray of light in the flint glass and the medium respectively. Also, let nfg and nm be the refractive indices of the flint glass and the medium respectively.
Data: dfg = 3 cm, nfg = 1.6, nm = 1.25,
Optical path = `"n"_"m" xx "d"_"m" = "n"_"fg" xx "d"_"fg"`
∴ `"d"_"m" = ("n"_"fg" xx "d"_"fg")/"n"_"m" = (1.6 xx 3)/1.25 = 3.84` cm
Thus, x cm = 3.84 cm
∴ x = 3.84
Solution 2
Given:
d1 = 3 cm, n1 = 1.6, n2 = 1.25
To find: Optical path in medium 2 (d2)
Formula: n1d1 = n2d2
Calculation:
From formula,
1.6 × 3 = 1.25 × d2
∴ d2 = `(1.6 xx 3)/1.25` = 3.84 cm
The value of x is 3.84 cm.
APPEARS IN
RELATED QUESTIONS
Draw the sketches to differentiate between plane wavefront and spherical wavefront.
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.
Define a wavefront.
If we put a cardboard (say 20 cm × 20 cm) between a light source and our eyes, we can't see the light. But when we put the same cardboard between a sound source and out ear, we hear the sound almost clearly. Explain.
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 \[\lambda_a and \lambda_f,\]
The inverse square law of intensity \[\left(\text{i.e. the intensity }\infty \frac{1}{r^2}\right)\] is valid for a ____________ .
A light wave can travel
(a) in vacuum
(b) in vacuum only
(c) in a material medium
(d) in a material medium only
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 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) \[\nu_B = \frac{1}{2}\left( \nu_A + \nu_C \right)\]
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 speed of yellow light in a certain liquid is 2.4 × 108 m s−1. Find the refractive index of the liquid.
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?
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.
A glass surface is coated by an oil film of uniform thickness 1.00 × 10−4 cm. The index of refraction of the oil is 1.25 and that of the glass is 1.50. Find the wavelengths of light in the visible region (400 nm − 750 nm) which are completely transmitted by the oil film under normal incidence.
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?
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?
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?
Monochromatic electromagnetic radiation from a distant source passes through a slit. The diffraction pattern is observed on a screen 2.50 m from the slit. If the width of the central maximum is 6.00 mm, what is the slit width if the wavelength is
(a) 500 nm (visible light)
(b) 50 µm (infrared radiation)
(c) 0.500 nm (X rays)?
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 ______.
