A single slit Fraunhoffer diffraction pattern is formed with white light.For what wavelength of light the third secondary maximum in the diffraction pattern coincides with the second secondary maximum in the pattern of red light of wavelength 6500 `Å`?

Options

A. 4400 `Å`
B. 4100 `Å`
C. 4642.8 `Å`
D. 9100 `Å`

Answer

C

Explanation

`x = ((2n + 1)lambda D)/(2a)`
For red light, x = `((4 + 1)D)/(2a) xx 6500 dot A`
For other light, `x = ((6 + 1)D)/(2a) xx lambda dot A`
x is the same for each.
`therefore 5 xx 6500 = 7 xx lambda Rightarrow lambda = (5)/(7) xx 6500 = 4642.8 dot A`.