Question

If the first-order maximum for monochromatic light falling on a double slit is at an angle of 10.0∘, at what angle is the second-order maximum?

Answer 1

The value is
`\theta_2 = 20.322^o`

Step-by-step explanation:

From the question we are told that

The angle of the first order maximum is
`\theta _1 = 10.0^o`

Generally the condition for constructive interference is

`dsin\theta = n \lambda`

Here d is the separation between the slit ,

n is the order of maxima with values n = 1, 2 , 3 ... for first , second , third ... order of maxima

Now for first order of maximum

`dsin\theta_1 = \lambda \ \ ... \ \ ( 1)`

=>
`dsin(10) = \lambda \ \ ... \ \ ( 1)`

Now for second order of maximum

`dsin\theta = 2\lambda \ \ ... \ \ ( 2)`

dividing equation 1 by 2

`(d sin (10))/(d sin (\theta_2 )) = (\lambda)/(2\lambda)`

`( sin (10))/( sin (\theta_2 )) = (1)/(2)`

=>
`2sin(10) = sin (\theta_2 )`

=>
`0.3473 = sin(\theta_2)`

=>
`\theta_2 = sin^(-1) [0.3473]`

=>
`\theta_2 = 20.322^o`