Question

Find the angles of the first three principal maxima above the central fringe when this grating is illuminated with 672 nm light.

Answer 1

Complete Question

A grating has 767 lines per centimetre.Find the angles of the first three principal maxima above the central fringe when this grating is illuminated with 672 nm light.

Answer:

The first is

`\theta_1 = 2.92^o`

The second is

`\theta _2 = 5.93^o`

The third is

`\theta _3 = 8.92^o`

Step-by-step explanation:

From the question we are told that

The number of lines per cm is
`I = 767 \ lines/cm = 76700 \ lines / m`

The wavelength is
`\lambda = 672nm = 672 *10^(-9) \ m`

Generally the condition for constructive interference is

`dsin (\theta ) = n\lambda`

Here d is the distance of separation of the slit which is mathematically represented as

`d = (1)/(l)`

`d = (1)/(76700)`

`d = 1.30*10^(-5) \ m`

So

`\theta_1 = sin^(-1) [( n \lambda )/( d) ]`

For the first angle n = 1

So

`\theta_1 = sin^(-1) [( 1 * 672 *10^(-9) )/( 1.30 *10^(-5)) ]`

`\theta_1 = 2.92^o`

For the second angle n = 2

So

`\theta_2 = sin^(-1) [( 2 * 672 *10^(-9) )/( 1.30 *10^(-5)) ]`

`\theta _2 = 5.93^o`

For the second angle n = 3

So

`\theta_3 = sin^(-1) [( 3 * 672 *10^(-9) )/( 1.30 *10^(-5)) ]`

`\theta _3 = 8.92^o`