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
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.
Is the colour of 620 nm light and 780 nm light same? Is the colour of 620 nm light and 621 nm light same? How many colours are there in white light?
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.
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?
Light is _______________ .
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 ____________ .
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.
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.
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?
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?
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)?
Light follows wave nature because ______
Young’s double-slit experiment is carried out using green, red and blue light, one colour at a time. The fringe widths recorded are WG, WR, and WB respectively then ______
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.
Light behaves as _________.
A ray is an imaginary line ______.
