Question

Light passes through a 0.15 mm-wide slit and forms a diffraction pattern on a screen 1.25 m behind the slit. The width of the central maximum is 0.75 cm. What is the wavelength of the light

Answer 1

The value is
`\lambda = 900 \ nm`

Step-by-step explanation:

From the question we are told that

The width of the slit is
`a = 0.15 \ mm = 0.00015 \ m`

The distance of the screen from the slit is D = 1.25 m

The width of the central maximum is
`y = 0.75 \ cm = 0.0075 \ m`

Generally the width of the central maximum is mathematically represented as

`y = (m * D * \lambda)/(a)`

Here m is the order of the fringe and given that we are considering the central maximum, the order will be m = 1 because the with of the central maximum separate's the and first maxima

So

`\lambda = (a y)/( m * D )`

=>
`\lambda = ( 0.000015 * 0.0075)/( 1 * 1.2 )`

=>
`\lambda = 900 *10^(-9) \ m`

=>
`\lambda = 900 \ nm`