Advertisements
Advertisements
प्रश्न
Show that the angular width of the first diffraction fringe is half that of the central fringe.
Advertisements
उत्तर
Let λ and a be the wavelength and slit width of diffracting system, respectively. Let O be the position of central maximum. Condition for the first minimum is given by
asinθ=mλ .....(1)
Let θ be the angle of diffraction.
As diffraction angle is small
∴ sinθ ≈ θ
For the first diffraction minimum, let θ = θ1
For the first minimum, take m =1
aθ1=λ
`=>theta_1=lambda/a`
Now, angular width AB = θ1
Angular width BC = θ1
Angular width AC = 2θ1
Width of central maximum = 2θ1
APPEARS IN
संबंधित प्रश्न
In Young' s experiment the ratio of intensity at the maxima and minima . in the interference pattern is 36 : 16. What is the ratio of the widths of the two slits?
In Young's double slit experiment, describe briefly how bright and dark fringes are obtained on the screen kept in front of a double slit. Hence obtain the expression for the fringe width.
A beam of light consisting of two wavelengths, 650 nm and 520 nm, is used to obtain interference fringes in a Young’s double-slit experiment.
Find the distance of the third bright fringe on the screen from the central maximum for wavelength 650 nm.
Write three characteristic features to distinguish between the interference fringes in Young's double slit experiment and the diffraction pattern obtained due to a narrow single slit.
In Young’s experiment interference bands were produced on a screen placed at 150 cm from two slits, 0.15 mm apart and illuminated by the light of wavelength 6500 Å. Calculate the fringe width.
The slits in a Young's double slit experiment have equal width and the source is placed symmetrically with respect to the slits. The intensity at the central fringe is I0. If one of the slits is closed, the intensity at this point will be ____________ .
If the source of light used in a Young's double slit experiment is changed from red to violet, ___________ .
In a Young's double slit experiment, two narrow vertical slits placed 0.800 mm apart are illuminated by the same source of yellow light of wavelength 589 nm. How far are the adjacent bright bands in the interference pattern observed on a screen 2.00 m away?
Wavefront is ______.
In Young's double slit experiment the slits are 0.589 mm apart and the interference is observed on a screen placed at a distance of 100 cm from the slits. It is found that the 9th bright fringe is at a distance of 7.5 mm from the dark fringe which is second from the center of the fringe pattern. Find the wavelength of the light used.
