Question

`In case of diffraction pattern of a single slit under polychromatic illumination first minima of wavelength lambda 1 is found to coincide with the second maxima of wavelength lambda 2 then`​

Answer 1

answer

lambda=2.5lambda2

explanation

n1×lambda1×D/d =n2×lambda×D/d

1×lambda1= (2n+1) /2 ×lambda2

1×lambda1= (2×2+1)/2 × lambda2

lambda 1=2.5 lambda 2

Answer 2

Diffraction pattern:

Explanation:

In diffraction patterns, the first minima of wavelength λ1 have coincided with the second maxima of wavelength λ2.

i.e. position of first minima = position of second maxima     ...(1)

The minima in the diffraction pattern is given as

$\displaystyle \frac{n\lambda_1\ D}{d}$         ...n =1, 2,3

Here n= 1

∴The position of first minima = $\displaystyle \frac{\lambda_1\ D}{d}$

The maxima in the diffraction pattern is given as

$\displaystyle \frac{(2n +1 )\lambda_2 \ D}{2d}$             ... n = 0, 1, 2,3, ...

Here n = 2

∴ The position of second maxima = $\displaystyle \frac{5\lambda_2 \ D}{2d}$

Put these values in the above equation(1)

$\displaystyle \frac{\lambda_1\ D}{d} = \displaystyle \frac{5\lambda_2 \ D}{2d}$

$\mathbf{2\lambda_1 = 5\lambda_2}$

This is the condition