Question

In a double-slit arrangement the slits are separated by a distance equal to 90 times the wavelength of the light passing through the slits. (a) What is the angular separation in radians between the central maximum and an adjacent maximum? rad (b) What is the distance between these maxima on a screen 49.0 cm from the slits?

Answer 1

a)θ =0.0109 rad

b)y=0.53 cm

Explanation:

a). Given that

Distance = 90 wavelength

d= 90 λ

As we know that

`sin\theta =(\lambda )/(d)`

θ =Angular separation

Now putting the values

`sin\theta =(\lambda )/(d)`

`sin\theta =(\lambda )/(90\lambda)`

θ = 0.63 °

θ =0.0109 rad

b)

Given that D= 49 cm

The distance y given as

`y=D\ tan\theta`

Now by putting the values

`y=D\ tan\theta`

`y=49* tan0.63^(\circ)`

y=0.53 cm