Question

A narrow monochromatic beam of light of intensity 1 is incident on a glass plate as shown in figure Another identical glass plate is kept close to the first one and parallel to it. Each glass plate reflects `25%` of the light incident on it and transmits intensities in the interference pattern formed by two beams obtained after one reflection at each plate.

Answer 1

`I` is the intensity of incident beam ab. The interfering waves. Are bc and ef, reflected from surface of plates 1 and 2, respectively.
Reflectoin coefficient of intensity
`r = 25% = 0.25`
Transmission coefficient of intensity,
`t = 75% = 0.75`
The intensity of beam bc, `I_(1) = 0.25 I = (1)/(4) I`
The intensity of beam `bd = 0.75 I`
The intensity of beam `de = 0.25 xx 0.75 I`
The intensity of beam ef,
`I_(2) = 0.75 xx 0.25 xx 0.75 I = (9)/(64) I`
Ratio of maximum and minimum intensities,
`(I_(max))/(I_(min)) = (a_(1) + a_(2))^(2) / (a_(1) - (a_(2))^(2)) =(a_(1)^(2) + a_(2)^(2)+ 2a_(1) a_(2))/(a_(1)^(2) - a_(1)^(2)-2 a_(1) a_(2))`
`=(I_(1) +I_(2) + 2sqrt((I_(1) I_(2))))/(I_(1) + I_(2) - 2sqrt((I_(1) I_(2))) )=((1)/(4) I + (9)/(64) I + 2((1)/(4)I xx(9)/(64 )I))/((1)/(4) I + (9)/(64) I- 2sqrt(((1)/(4) I xx (9)/(64) I))`
`((49//64)I)/((1//64)I) = (49)/(1)`.