Question

In a double-slit arrangement the slits are separated by a distance equal to 120 times the wavelength of the light passing through the slits. (a) What is the angular separation between the central maximum and an adjacent maximum

Answer 1

In a double-slit arrangement the slits are separated by a distance equal to 120 times the wavelength of the light passing through the slits. (a) What is the angular separation between the central maximum and an adjacent maximum(b) What is the distance between these maxima on a screen 5.79m from the slits?

Answer:

a

`\theta  =  0.476 ^ o`

b

`y =  0.0481 \ m`

Step-by-step explanation:

From the question we are told that

The slit separation is
`d =  120 \lambda`

Here
`\lambda` is the wavelength of the light

Generally the condition for constructive interference is mathematically represented as

`dsin (\theta) =  m *  \lambda`

=>
`\theta  =  sin^(-1) [(n *  \lambda)/( d ) ]`

=>
`\theta  =  sin^(-1) [(n *  \lambda)/(  120 \lambda ) ]`

Here n is the order of maxima which is 1 given that we are considering the central maximum and an adjacent maximum

So

`\theta  =  sin^(-1) [(1)/(  120) ]`

=>
`\theta  =  0.476 ^ o`

Generally given that the distance of the screen is D = 5.79 m from the slit then the distance between these maxima is mathematically represented as

`y = D tan (\theta )`

=>
`y = 5.79 *  tan (0.476)`

=>
`y =  0.0481 \ m`