Question

A lens having focal length f gives Fraunhofer type diffraction pattern of a slit having width a. If wavelength of light is λ, the distance of first dark band and next bright band from axis is given by ____________.

Options

• `a/lambdaf`

• `lambda/af`

• `lambda/(af)`

• `alambdaf`

Answer 1

A lens having focal length f gives Fraunhofer type diffraction pattern of a slit having width a. If wavelength of light is λ, the distance of first dark band and next bright band from axis is given by `lambda/af`.

Explanation:

Here for minima,

a `sin theta = nlambda`

For first dark band, n = 1

`therefore sin theta = lambda/a or theta =lambda/a  .... (because sin theta = theta  "for small angles")`

Let distance of first dark band from axis be y then angle of diffraction `theta` is given by `x/f`

`therefore x/f = lambda/a or  x = lambda/af`