Question

In a double-slit arrangement the slits are separated by a distance equal to 150 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

Complete Question

In a double-slit arrangement the slits are separated by a distance equal to 150 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 57.9 cm from the slits?

Answer:

a

`\theta = 0.3819^o`

b

`y = 0.00386 \ m`

Step-by-step explanation:

From the question we are told that

The slit separation is
`d = 150 \lambda`

The distance from the screen is
`D = 57.9 \ cm = 0.579 \ m`

Generally the condition for constructive interference is mathematically represented as

`dsin (\theta ) = n * \lambda`

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

where n is the order of the maxima and value is 1 because we are considering the central maximum and an adjacent maximum

and
`\lambda` is the wavelength of the light

So

`\theta = sin ^(-1) [( 1 * \lambda )/( 150 \lambda ) ]`

`\theta = 0.3819^o`

Generally the distance between the maxima is mathematically represented as

`y = D tan (\theta )`

=>
`y = 0.579 tan (0.3819 )`

=>
`y = 0.00386 \ m`