Question

Red light has a wavelength of 700. nm illuminates a slit of width 0.750 mm. The slit is 1.58 m from a screen. Where is the first minimum in the diffraction pattern on the screen relative to the center of the central maximum?

A. 1.1.47x10-3 m
B. none of the choices
C. 1.07x10-3 m
D. 1.58 m

Answer 1

A. 1.47x10-3 m

Step-by-step explanation:

The distance to the nth maximum from the central band is given by

`y = n(\lambda L)/(d)`

where
`\lambda` is the wavelength of light,
`L` is the distance to the screen, and
`d` is the slit separation.

Now, the first maximum appears at
`n=1`; therefore,
`y` becomes

`y = (\lambda L)/(d)`

and since in our case
`\lambda = 700*10^(-9) m`,
`L = 1.58m`, and
`d = 0.750*10^(-3)m`, we get:

`y = (700*10^(-9) (1.58))/(0.750*10^(-3)m)`

`\boxed{y=1.47*10^(-3)m.}`

which we see is choice A from the options.