## In Young’s double slit experiment the separation d between the slits is 2 mm , the wavelength λ of the light used…

Q: In Young’s double slit experiment the separation d between the slits is 2 mm , the wavelength λ of the light used 5896 A° and distance D between the screen and slits is 100 cm . It is found that angular width of fringe is 0.20° . To increase the angular fringe width to o.21° (with same λ and D) the separation between the slits needs to be changed to

(a) 2.1 mm

(b) 1.7 mm

(c) 1.9 mm

(d) 1.8 mm

Ans: (d)

Sol: Angular fringe width $\displaystyle \theta = \frac{\lambda}{d}$

$\displaystyle 0.20 = \frac{\lambda}{2}$

$\displaystyle 0.21 = \frac{\lambda}{d}$

On solving ,

d = 1.9 mm

## In Young’s double slit experiment, using monochromatic light, fringe pattern shifts by a certain distance on the screen when a mica sheet…

Q: In Young’s double slit experiment, using monochromatic light, fringe pattern shifts by a certain distance on the screen when a mica sheet of refractive index 1.6 and thickness 1.964 μm is introduced in the path of one of the two waves.Now mica sheet is removed and distance between slit and screen is doubled, distance between successive maxima or minima remains unchanged. The wavelength of the monochromatic light used in the experiment is

(a) 4000 Å

(b) 5500 Å

(c) 5892 Å

(d) 6071 Å

Ans: (c)

Sol: Here, µ = 1.6 , t =1.964 µm = 1.964 × 10-6 m

Additional path diff. introduced on account of mica sheet

=(µ-1)t = x d/D

When distance between the slit and screen is doubled, then fringe width

β =(2λ D)/d

As β = x

$\displaystyle \frac{2 \lambda D}{d} = \frac{(\mu -1)t D}{d}$

$\displaystyle \lambda = \frac{(\mu – 1) t}{2}$

$\displaystyle \lambda = \frac{(1.6 – 1) 1.964 \times 10^{-6}}{2}$

λ = 5892 × 10-10 m

λ = 5892 A °

## In Young’s double slit experiment, the two slits act as coherent sources of equal amplitude a and of wavelength λ…

Q: In Young’s double slit experiment, the two slits act as coherent sources of equal amplitude a and of wavelength λ . In other experiment with the same set up, the two slits are sources of equal amplitude a and wavelength λ , but are incoherent. The ratio of intensity of light at the mid point of the screen in the first case to that in the second case is

(a) 2 : 1

(b) 1 : 2

(c) 2 : 4

(d) 4 : 3

Ans: (a)

Sol : When sources are coherent, intensity at mid point

Imax = (a+a)2 = 4 a2

When source are incoherent, no interference occurs. Intensity at mid point,

I= I1 + I2

I = a2 + a2 = 2 a2

Imax/I = (4a2 )/(2a2 ) = 2∶1

## In the ideal double slit experiment, when a glass plate of refractive index 1.5 and thickness t is introduced in the path…

Q: In the ideal double slit experiment, when a glass plate of refractive index 1.5 and thickness t is introduced in the path of one of the interfering beams of wavelength λ , the intensity at the position of central max. remains unchanged. Minimum thickness of glass plate is

(a) 2 λ

(b) 2 λ/3

(c) λ/3

(d) λ

Ans: (a)

Sol: Path difference due to slab should be integral multiple of λ ,

i.e., Δx = (µ-1)t = n λ

where n = 1 , 2 , 3 ,……

$\displaystyle t = \frac{n \lambda}{(\mu – 1)}$

For minimum value of t ;n=1

$\displaystyle t = \frac{ \lambda}{(1.5 – 1)}$

t = 2 λ

## In a Young’s double slit experiment, the slits are 2 mm apart and are illuminated with a mixture of two wavelength…

Q: In a Young’s double slit experiment, the slits are 2 mm apart and are illuminated with a mixture of two wavelength λ = 12000 Å and λ’= 10000 Å . At what minimum distance from the common central bright fringe on a screen 2 m from the slits will a bright fringe from one interference pattern coincide with a bright fringe from the other?

(a) 3.2 mm

(b) 6.0 mm

(c) 7.2 mm

(d) 9.2 mm

Ans: (b)

Sol: $\displaystyle y = \frac{n \lambda D}{d} = \frac{(n+1)\lambda’ D}{d}$

$\displaystyle n \times 12000 = (n+1)\times 10000$

n = 5

$\displaystyle y = \frac{n \lambda D}{d}$

$\displaystyle y = \frac{5 \times 12000 \times 2}{2\times 10^{-3}}$

= 6 mm