Question

if a green Ray of light is replaced by a blue light for a given angle of incidence on the glass slab how does the lateral shift change


PLSS ANS BRAINLISTS​

Answer 1

suppose the slab has a certain thickness, say d. From Snell's law about refraction, calling θi the angle between the incoming ray and the normal to the surface, ni the refractive index of the medium outside the slab, nm the refractive index inside the slab and θm the angle between the ray in the slab and the normal to the surface:

nmsinθm=nisinθi

you can derive the angle θm:

sinθm=ninmsinθi

Then, from basic trigonometry, you know that:

sin2θm+cos2θm=1 ⇒ cosθm=1−sin2θm−−−−−−−−−√

and, with d as defined and l length of the path of the ray inside the slab, you can write:

d=l⋅cosθm ⇒ l=dcosθm

Calling x the lateral displacement you are asking for:

x=l⋅sinθm

By substituting in this equation, you can get your result as an expression of the angle of incidence, the refractive indexes and the thickness of the slab.