Advertisements
Advertisements
प्रश्न
A beam of light consisting of two wavelengths, 800 nm and 600 nm is used to obtain the interference fringes in a Young's double slit experiment on a screen placed 1 · 4 m away. If the two slits are separated by 0·28 mm, calculate the least distance from the central bright maximum where the bright fringes of the two wavelengths coincide.
Advertisements
उत्तर
Given: −
λ1 = 800 nm = 800 × 10−9 m
λ2 = 600 nm = 600 × 10−9 m
D = 1.4 m
d = 0.28 mm = 0.28 × 10−3 m
Let n1th maximum corresponds to λ1 coincides with n2th maximum corresponds to λ2. Then,
`n_1(lambda_1D)/d =n_2 ((lambda_2)D)/d`
`or,n_1/n^2 =lambda^2/lambda^1 = 600/800 =3/4`
The minimum integral value of n1 is 3 and of n2 is 4. Therefore, the minimum value of y is,
`y_(min) = n_1(lambda_1D)/d=(3 xx 800 xx 10^-9 xx 1.4)/((0.28) xx 10^-3)`
`y_(min) =12mm`
संबंधित प्रश्न
(i) In Young's double-slit experiment, deduce the condition for (a) constructive and (b) destructive interferences at a point on the screen. Draw a graph showing variation of intensity in the interference pattern against position 'x' on the screen.
(b) Compare the interference pattern observed in Young's double-slit experiment with single-slit diffraction pattern, pointing out three distinguishing features.
Using analytical method for interference bands, obtain an expression for path difference between two light waves.
If Young's double slit experiment is performed in water, _________________ .
A plate of thickness t made of a material of refractive index µ is placed in front of one of the slits in a double slit experiment. (a) Find the change in the optical path due to introduction of the plate. (b) What should be the minimum thickness t which will make the intensity at the centre of the fringe pattern zero? Wavelength of the light used is \[\lambda.\] Neglect any absorption of light in the plate.
In Young's double slit experiment using monochromatic light of wavelength 600 nm, 5th bright fringe is at a distance of 0·48 mm from the centre of the pattern. If the screen is at a distance of 80 cm from the plane of the two slits, calculate:
(i) Distance between the two slits.
(ii) Fringe width, i.e. fringe separation.
When a beam of light is used to determine the position of an object, the maximum accuracy is achieved, if the light is ______.
Two balls are projected at an angle θ and (90° − θ) to the horizontal with the same speed. The ratio of their maximum vertical heights is:
Young's double slit experiment is made in a liquid. The 10th bright fringe lies in liquid where 6th dark fringe lies in vacuum. The refractive index of the liquid is approximately
In a Young’s double slit experiment, the source is white light. One of the holes is covered by a red filter and another by a blue filter. In this case ______.
The maximum number of possible interference maxima for slit-separation equal to twice the wavelength in Young's double-slit experiment is ______.
