Light passes through a single slit of width 8.32x10^-5 m. The first (m=1) diffraction minimum occurs at an angle of 0.347. What is the wavelength of the light in nanometers?

(Hint: The answer will be between 400 and 700 nm.)

theta = m wavelength / silt width

gives angular position of minimas where m = 1,2,3 ...

As

0.347° = pi/180 * 0.347 rad = 0.006 rad

using above formula

0.006 = 1 * wavelength / 8.32 * 10^-5 m

wavelength = 0.006 * 8.32 * 10^ - 5 m

= 0.04992 * 10^ - 9 m

= 499 * 10^ - 9m

=499 nm

which is almost 500 nm