1. If one side of a thin lens is filled with ethyl alcohol and the other side is filled with water, find the front and the second focal lengths of the lens. Here R1 and R2 are the radii of curvature of the lens's surfaces, and n1, n, and n2 are the refractive indices of the ethyl alcohol, the lens, and the water, respectively.
2. Given a positive (convex) thin lens with a refractive index of n = 1.5 , assume that one side of the lens is filled with air ( n = 1) and the other side is filled with water ( n = 1.33). The radii of curvature of the lens's surface are R1 =10 cm and R2 =15 cm, respectively.
Calculate the front and back focal lengths of the lens.
3. A convenient way to measure the focal length of a positive lens makes use of the following fact. If a pair of conjugate object and (real) image points (S and P) are separated by a distance L > 4f, there will be two locations of the lens, a distance d apart, for which the same pair of conjugates obtain. Show that
f =((L2-d2)/4L)
Note that this avoids measurements made specifically from the vertex, which are generally not easy to do.
4. A compound lens is composed of two thin lenses separated by 10 cm. The first of these has a focal length of +20 cm, and the second a focal length of -20 cm. Determine the focal length of the combination and locate the corresponding principal points. Draw a diagram of the system.
5. In the above problem, if an object is located 30 cm on the left side of the first lens.
a) Find the final image position and lateral magnification using twice imaging approach.
b) Repeat Part a using effective focal length and principal plane approach
c) Check your result using ray diagram.
d) Is the final image real or virtual?
e) Is the final image inverted or erect?
6. Two converging lenses having focal lengths of 10.0 cm and 20.0 cam are located 50.0 cm apart as shown below. The final image is to be located between the lenses at the position indicated.
a) How far to the left of the first lens should the object be positioned?
b) What is the overall magnification?
c) Is the final image erect or inverted?
