Question

Monochromatic light falls on two very narrow slits 0.047 mm apart. Successive fringes on a screen 6.60 m away are 8.9 cm apart near the center of the pattern.

Determine the wavelength and frequency of the light.

Answer 1

Answer::

`\lambda = 634 nm`

`f = 4.73 *10^(14) \ Hz`

Step-by-step explanation:

From the question we are told that

The distance of separation is
`d = 0.047 \ mm = 0.047 *10^(-3) \ m`

The distance of the screen is
`D = 6.60 \ m`

The width of the fringe is
`y = 8.9 \ cm = 0.089 \ m`

Generally the width of the width of the fringes is mathematically represented as

`y = (\lambda * D )/(d )`

=>
`\lambda = (y * d )/(D )`

=>
`\lambda = ( 0.089 * (0.047 *10^(-3)) )/(6.60 )`

=>
`\lambda = 634 *10^(-9)`

=>
`\lambda = 634 nm`

Generally the speed of light is mathematically represented as

`c = f * \lambda`

=>
`f= ( c)/(\lambda )`

=>
`f= ( 3.0 *10^(8))/(634 *10^(-9))`

=>
`f = 4.73 *10^(14) \ Hz`