Question

1. The refractive index n of transparent acrylic plastic (full name Poly(methyl methacrylate)) depends on the color (wavelength) of the light passing through it. At wavelength 486.1 nm (blue, designated with letter F) -> nF=1.497, and at wavelength 656.3 nm (red, designated with letter C) -> nC=1.488. Two beams (one of each wavelength) are prepared to coincide, and enter the flat polished surface of an acrylic block at angle of 45 arc degree measured from the normal to the surface. What is the angle between the blue beam and the red beam in the acrylic block?

2. Consider a lens with focal length f. What will be the distance between the lens and the image if the object is placed further from the lens at distance of 3 focal lengths?

Answer 1

1)

sin i / sin r = n

For blue beam,
sin r = sin i / n = sin 45 / 1.497

r = 28.20 deg

For red beam,
sin r = sin i / n = sin 45 / 1.488

r = 28.376 deg

thus, difference in angle = 28.376 - 28.20 = 0.176 degrees

2)

Using lens formula:
1/v - 1/u = 1/f

1/v = 1/f + 1/u

For converging lens,

1/v = 1/f - 1/3f

1/v = 2/3f

v = 3f/2

For diverging lens,

1/v = -1/f - 1/3f

1/v = -4/3f

v = -3f/4