A ray of light is incident on one face of a glass prism that has the shape of an

Question

A ray of light is incident on one face of a glass prism that has the shape of an isosceles triangle, as shown in the figure. The index of refraction of the glass is n, arid the angle at the apex of the triangle is alpha. Find an expression for the angle theta such that the ray in the glass is parallel with the base of the prism. An object and a screen are a distance L apart. A converging lens, with focal length f, such that L > 4f, is placed between the object and the screen. There are two positions where the lens can be placed to give an image of the object on the screen. In one case, the image is magnified. In the other case, it is diminished. In both cases, the image is inverted. If the ditance between these two positions is D, find an expression for the focal length of the lens in terms of L and D.

Explanation / Answer

1 )

using snell's law

n1sintheta = n2sin*phi

n1 = 1 ( air refrective index = 1)

n2 = n

sintheta = n*sinphi

phi is angle in the prism ,the angle between the light path and the normal to the prism

Since the light path is parallel to the base, if we call beta the angle  of the two isosceles angles, then the light path makes the same angle beta with respect to the wall of the prism.

beta + phi = 90

the triangle is isosceles 2beta + alpha = 180

beta = 90 -phi

phi = alpha/2

theta = sin^-1(n*sinphi)

theta = sin^-1(n*sin(alpha/2))

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