Question

A thin film of MgF2 (n = 1.38) coats a piece of glass. Constructive interference is observed for the reflection of light with wavelengths of 460 nm and 613 nm .

     A. What is the thinnest film for which this can occur? (Express your answer with the appropriate units.)

d =

Answer 1

n = 1.38

the thickness of a film t= m* /2n for   Constructive interference

for = 460nm

t1 =m1*460 / ( 2*1.38 )

for = 613 nm

t2 = m2*613 /( 2*1.38)

since the thickness is constant so comparre these two

t1 = t2

m1*460 / ( 2*1.38 ) =m2*613 / ( 2*1.38 )

m1*460 = m2*613

m2 = 0.750 *m1

m2 /m1 = 3/4

now we have to guess  

take m1 = 4 and m2 = 3

t1 = 4*460 / ( 2*1.38 ) = 666.666667 ​nm

t2 = 3*613 /( 2*1.38) =666.304348 nm

so out answer = 666.30 nm

let me know in a comment if there is any problem or doubts​