Question

In a Young's double slit experiment with slit separation 0.1 mm, one observes a bright fringe at angle 1/40 rad by using light of wavelength λ1 . When the light of wavelength λ2 is used a bright fringe is seen at the same angle in the same set up. Given that λ1 and λ2 are in visible range (380 nm to 740 nm), their values are :

(1) 380 nm, 525 nm
(2) 625 nm, 500 nm
(3) 380 nm, 500 nm
(4) 400 nm, 500 nm

Answer 1

The correct values of the wavelengths λ1 and λ2 are 380 nm and 500 nm, respectively. Option number 3 is correct.

Step-by-step explanation:

In a Young's double slit experiment, the bright fringes are formed due to the interference of light waves. The condition for constructive interference at an angle θ is given by dsinθ = mλ, where d is the slit separation, θ is the angle, m is the order of the bright fringe, and λ is the wavelength of light.

In this question, the same bright fringe is observed at angle 1/40 rad with two different wavelengths of light, λ1 and λ2.

We can use the given information to find the ratio of the wavelengths:

d sinθ = mλ

For both wavelengths, the slit separation and angle are the same, so we have:

d sinθ = mλ1

d sinθ = mλ2

Dividing these two equations, we get:

(λ1/λ2) = 1

Therefore, the values of λ1 and λ2 are the same, and the correct option is (3) 380 nm, 500 nm.