Question

A slit S is illuminated by a monochromatic suorce of light to give two coherent sources P₁ and P₂ . These give a dark band at the point R on the screen as shown in figure.

1. Write the formula to find out bandwidth. 

2. What relationship must exist between the length P₁ R and P₂ R?

3. Can interference fringes be produced by using two identical bulbs?

4. If the distance between P₁ and P₂ is 1 mm and the screen is placed in 1m away, what is the fringe separation for a light of wavelength 5 × 10^-7 m?

Answer 1

1. β = \(\frac{λD}{d}\)

2. The condition for dark fringe is P₂R – P₁R = (2n -1)\(\frac{λ}{2}\) where n = 1,2, 3, etc.

3. No. They are not coherent sources.

4.  β =  \(\frac{λD}{d}\) = \(\frac{1\times5\times10^{-7}}{10^{-3}}\) = 5 x 10^-4 = 0.5 mm