A single slit Fraunhoffer diffraction patternn 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 patternn of red light of wavelength 6300 Å?

Options

A. 4400 Å
B. 4800 Å
C. 4500 Å
D. 5500 Å

Answer

C

Explanation

The angular posiition of the nth secondary maxima on the screen is given by
`sintheta=theta=((2n+1)lamda)/(2a)`
`therefore`The disctance of the nth secondary maxima from the central maximum is `x_(n)=D theta=((2n+1)lamdaD)/(2a)`
`therefore`for red light and for n=2,
`x_(2)=((2xx2+1)Dlamda_(R))/(2a)=(5Dlamda_(R))/(2a)`
and for other light, `n=3` and
`x_(3)=((2xx3+1)lamdaD)/(2a)=(7lamdaD)/(2a)`
But it is given that `x_(2)=x_(3)" "therefore 5lamda_(R)=7lamda`
`therefore lamda=(5lamda_(R))/(7)=(5)/(7)xx6300=4500` Å