## Question

The fringe-width is obtained as 0.060 cm on using light of wavelength 5000Ã… in Young’s experiment. What value of wavelength of light should be taken so that the width of the fringe on the screen could be obtained as 0.040 m, if the distance of screen from the slit is halved?

### Solution

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In the first case, fringe-width

Where *D* is the distance of the screen and *d* is separation between the slits. In the second case, taking *D*/2 in place of *D*, the new fringe-width is

Dividing eq. (ii) by eq. (i), we get

Putting the values:

#### SIMILAR QUESTIONS

A light-ray of 6000 Ã… wavelength travelling in vacuum enters a medium of refractive index 1.5. Find the speed and the wavelength of the ray in the medium.

The absolute refractive index of air is 1.0003 and the wavelength of yellow light in vacuum is 6000 Ã…. Find the thickness of air column which will have one more wavelength of the yellow light than in the same thickness of vacuum.

The number of waves in a 4-cm thick strip of glass is the same as in 5-cm water, when the same monochromatic light travels in them. If the refractive index of water be 4/3, what will be of glass?

What is the content of energy in *X*-ray photon of wavelength 10 Ã…? Given J-s,

Calculate de-Broglie wavelength for an electron and a proton moving with the same speed of 10^{5} m/s. (*m _{e}* = 9.1×10

^{ –31}kg,

*m*= 1.67 × 10

_{p}^{ –27}kg and

*h*= 6.63 × 10

^{ –34}Js).

The ratio of intensities of two waves is 25:16. What is the ratio of amplitudes? If these two waves produce interference, then find the ratio of maximum and minimum intensities.

Two waves of same frequency have amplitude in the ratio 2:1. Find the ratio of the maximum and the minimum amplitudes and intensities in the region of interference.

Two coherent sources *X* and *Y* of light of wavelength

λ = 6.2 × 10^{ –5} cm, produce interference. If both the sources are in the same phase and *P* is an arbitrary observation point, then calculate *XP* – *YP*when the point *P* is (i) At the bright band of 10^{th} order, (ii) At the dark band between third and fourth order maxima.

In Young’s experiment on interference of light a fringe of width 0.04 cm is obtained on a screen placed at a distance of 50 cm from the slits when the wavelength of the light used is 5000 Ã…. If the distance of the screen from the slits remains unchanged, what will be the width of the fringe if light of wavelength 4000 Ã… is used?

In a two-slit experiment with monochromatic light, fringes are obtained on a screen placed at some distance from the slits. If the screen is moved by towards the slits, the change in fringe-width is . If the distance between the slits is 10^{–3 }

M, calculate the wavelength of the light used.