Hello could somebody please answer the question 2 with your

Hello, could somebody please answer the question #2 with your work and explanation for your answers. Thank you!
Geometrical Optics

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?

Answer:

This problem concerns Snell\'s Law, which is:

n1*sin(i) = n2*sin(r), where n1, n2 are the indices of refraction, i is the incident angle, and r is the refracted angle.

So, all you need to do is determine the refracted angle for each beam, and then take the difference.

For red: n1=1, i = 45, n = 1.497. So, solving for r....

n1*sin(i) = n2*sin(r)

1*sin(45)=1.497*sin(r)

r=28.16deg

For blue: n1 = 1, i = 45, n = 1.488.

1*sin(45)=1.488*sin(r)

r=28.35deg

Thus, the angle between these two is 28.35-28.16=0.19deg

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?

Solution

object distance s = 3f

focal length = f

image distance = s1 =?

1/f = 1/s + 1/s1     =   1/s1 = 1/f - 1/3f

   image distance   s1 = 1.5 f