Fringe Width in YDSE

Q. Consider a plane inclined at an angle ${45}^{\circ }$ with the horizontal has two slits $S_{1}and{S}_2$ separated by a distance $d=\sqrt{2}\text{mm}$. The screen is placed at a distance of $D=10\text{m}$ from the midpoint of the slits, as shown in the figure. A parallel monochromatic light beam of wavelength $5000\dot{A}$ is incident on the slits as shown. If the fringe width of interference pattern on the screen is $k\times {10}^{-3}\text{m}$, then the value of $k$ is .

Q. The Young's double slit experiment is performed with blue light and green light of wavelength $4360\dot{A}$ and $5460\dot{A}$ a respectively. If X is the distance of $4^{th}$ maxima, from the central one, then:

1. $X_{blue}=X_{green}$
2. $X_{blue}>X_{green}$
3. $X_{blue}<X_{green}$
4. $\frac{X_{blue}}{X_{green}}=\frac{5460}{4360}$

Q. In Young’s double slit experiment, the distance between the slits is 0.2 mm and the distance of the screen from the slits is 2 m. If light of wavelength 500 nm is used, find the number of fringes formed between two points separated by 1 cm on the screen.

1. 1
2. 2
3. 4
4. 3

Q. Monochromatic light from a narrow slit illuminates two narrow slits 0.3 mm apart, producing an interference pattern with bright fringes 1.5 mm apart on a screen 75 cm away. Find the wavelength of the light. Find the fringe width if (a) the distance of the screen is doubled and (b) the separation between the slits is doubled?

1. 600 nm, 3 mm, 0.75 mm
2. 400 nm. 1 mm, 0.5 mm
3. 600 nm, 2 mm, 0.75 mm
4. 400 nm, 1mm, 2 mm
   

Q.

Fringe width observed in the Young's double-slit experiment is $\beta$ . If the frequency of the source is doubled, the fringe width will

1. $becomes\frac{\beta }{2}$
2. $becomes\frac{3\beta }{2}$
3. $Remain\beta$
4. $becomes2\beta$

Q. The fringe width changes from 0.24 mm to 0.3 mm when the screen is moved by 20 cm away from the slits separated by 2 mm. calculate the wavelength of light used.

1. 400 nm
2. 500 nm
3. 600 nm
4. 700 nm

Q. In the double-slit experiment, the distance of the first dark fringe from the central line is 1mm. The distance of the $2^{nd}$ bright fringe from the central line is

1. 6mm
2. 4mm
3. 12mm
4. 16mm

Q. In Young's double slit experiment the phase difference between the waves reaching the central fringe and fourth dark fringe will be

1. $6\pi$
2. $zero$
3. $4\pi$
4. $7\pi$

Q. Two slits separated by 0.200 mm are to be used in Young’s double – slit experiment. Immediately behind the slits in a lens of focal length 0.500 m used to form the interference pattern on a screen located in the focal plane of the lens. What is wavelength of a monochromatic light source used to illuminate the slits if adjacent maxima of the interference pattern are separated by 1.00 mm?

1. 500 nm
2. 400 nm
3. 600 nm
4. 700 nm

Q. $S_1,S_2$ are two coherent sources of light. P is a point on the screen such that $S_{2}P-S_{1}P$ = 0.01029 cm. Wave length of light used is $6000\dot{A}$. The order of the fringe formed at P is

1. 172, bright
2. 171, bright
3. 173, dark
4. 172, dark