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? - Physics

Advertisements
Advertisements
Numerical

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 that 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`

`"v" = (3 xx 10^8)/1.33 = 2.26 xx 10^8  "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 xx 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.

  Is there an error in this question or solution?
Chapter 10: Wave Optics - Exercise [Page 383]

APPEARS IN

NCERT Physics Class 12
Chapter 10 Wave Optics
Exercise | Q 10.1 | Page 383
NCERT Physics Class 12
Chapter 10 Wave Optics
Exercise | Q 1 | Page 383

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

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.


TV signals broadcast by a Delhi studio cannot be directly received at Patna, which is about 1000 km away. But the same signal goes some 36000 km away to a satellite, gets reflected and is then received at Patna. 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?


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 \[\lambda_a   and   \lambda_f,\]


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 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.


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.


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°.


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.

  1. What is the angular separation in radians between the central maximum and an adjacent maximum?
  2. What is the distance between these maxima on a screen 50.0 cm from the slits?

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?


Choose the correct option:

In Young's double-slit experiment, a thin uniform sheet of glass is kept in front of the two slits, parallel to the screen having the slits. The resulting interference pattern will satisfy:


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 546 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)?


When light travels from an optically rarer medium to an optically denser medium, the speed decreases because of change in ______ 


Light follows wave nature because ______ 


The path difference between two waves meeting at a point is (11/4)λ. The phase difference between the two waves is ______


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


Emission and absorption is best described by ______.


Light appears to travel in straight lines since


State the theories which were proposed to explain nature of light.


Share
Notifications



      Forgot password?
Use app×