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 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 :

A. 625 nm, 500 nm
B. 380 nm, 525 nm
C. 380 nm, 500 nm
D. 400 nm, 500 nm

Answer 1

In Young's double-slit experiment, the angle of bright fringes can be calculated using the formula ∂x = m(λ/d), where m is the order of the fringe, λ is the wavelength of light, and d is the distance between the slits.

Step-by-step explanation:

In Young's double-slit experiment, the formula for the angle of bright fringes is given by ∂x = m(λ/d), where m is the order of the fringe, λ is the wavelength of light, and d is the distance between the slits. According to the given question, we have a bright fringe at angle 1/40 rad for both λ₁ and λ₂. We can set up the equations as follows:

∂x = m(λ₁/d) = 1/40 rad

∂x = m(λ₂/d) = 1/40 rad

We can solve these equations to find the values of λ₁ and λ₂:

λ₁ = d/40

λ₂ = d/40

Therefore, the values of λ₁ and λ₂ are both d/40, where d is the distance between the slits.