Advertisements
Advertisements
प्रश्न
Show that the angular width of the first diffraction fringe is half that of the central fringe.
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 double slit experiment, deduce the conditions for obtaining constructive and destructive interference fringes. Hence, deduce the expression for the fringe width.
Using monochromatic light of wavelength λ in Young’s double slit experiment, the eleventh dark fringe is obtained on the screen for a phase difference of ______.
A parallel beam of light of wavelength 500 nm falls on a narrow slit and the resulting diffraction pattern is observed on a screen 1 m away. It is observed that the first minimum is a distance of 2.5 mm away from the centre. Find the width of the slit.
Suppose white light falls on a double slit but one slit is covered by a violet filter (allowing λ = 400 nm). Describe the nature of the fringe pattern observed.
If the source of light used in a Young's double slit experiment is changed from red to violet, ___________ .
Two slits in Young's interference experiment have width in the ratio 1 : 2. The ratio of intensity at the maxima and minima in their interference 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:
A projectile can have the same range R for two angles of projection. If t1 and t2 be the times of flight in two cases, then what is the product of two times of flight?
Using Young’s double slit experiment, a monochromatic light of wavelength 5000Å produces fringes of fringe width 0.5 mm. If another monochromatic light of wavelength 6000Å is used and the separation between the slits is doubled, then the new fringe width will be ______.
In Young's double slit experiment the two slits are 0.6 mm distance apart. Interference pattern is observed on a screen at a distance 80 cm from the slits. The first dark fringe is observed on the screen directly opposite to one of the slits. The wavelength of light will be ______ nm.
