A glass lens is coated on one side with a thin film of magnesium fluoride (MgF2)

Question

A glass lens is coated on one side with a thin film of magnesium fluoride (MgF2) to reduce reflection from the lens surface (figure below). The index of refraction of MgF2 is 1.38; that of the glass is 1.50. Assume that the light is perpendicular to the lens surface and the coating eliminates the reflection of light of wavelength 550 nm at normal incidence.

(a) Calculate the percentage by which reflection is diminished by the coating at 405 nm.
______________ %

(b) Calculate this percentage for a wavelength of 690 nm.
_____________ %

Explanation / Answer

refraction index of MgF2 = 1.38
at normal incidence , wavelength of the light reflection =550 nm
from ,thin film interference
L =/4

a)

L_1 =550 nm/4*1.38 =99.63 nm 100 nm
L_2 =405 nm
(L_2/L_1)*100 405 %(so incident light completely reflected back)

b)

L_3 =690 nm/4*1.38 =125 nm
(L_3/L_1)*100 =125.43 nm 125% (so incident light completely reflected back)

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