a right angled prism of refractive index n has a plate of refractive index n1 so that n1 less than - Physics - Ray Optics And Optical Instruments

Question

a right angled prism of refractive index n has a plate of
refractive index n1 so that n1 less than n ,cemented to its
diagonal face the assembly is in air a ray is incident on AB

1) calculate the angle of incidence at AB for which the ray strikes
the diagonal face at the critical angle
2)assuming n=1 352 calculate the angle of incidence at AB for which
the refracted ray passes through the diagonal face undeviated
PLS ANS FAST

Pintu B. · Accepted Answer

Dear Student ,
 sin c = n1 / n (90°– r1) + 45 + (90° – c) = 180°r1 = 45°– c   sin i / sin r1 = n sin i = n sin r1 = n sin (45°–c)  = n (sin 45 cos c – cos 45 sin c)  = n/2 (cos c – sin c)  = n/2 ([ 1 – sin2C] – sin c)  = 1/2 (n2 – n12 ) – n1  ⇒i = sin-1 1/2 (n2 – n12 ) – n1 r2= 0  &  r1 + r2 = 45°r1 = 45° sin i / sin r1 = n sin i = n sin r1= 1·352 sin 45 = 0·956 ⇒ i = sin-1 (0·956) = 72·58

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