Find the matrix of the system of the three lenses shown below and show that they form a telescopic system with positive angular magnification.  Solve for m_q the case in which f₁ = 20 cm, f_i = 2 cm and f₂ = 5 cm.

A Ramsden eyepiece consists of two equal focal length lenses, f₁.  If the separation is equal to f₁, chromatic aberration is minimized.  In practice the lenses are usually moved closer together.  Calculate the position of the focal points and the focal lengths of the eyepiece in the case in which d = (3/4)f₁.

One simple form of the astronomical reflecting telescope is shown above.  A parallel beam of light reflected from the spherical concave mirror with radius R is brought to the second focal point, F'_M, of this mirror after further reflection by a small plane mirror.  The focal point F' is also the first focal point F_L of the eyepiece lens.  The plane mirror is sufficiently small so that it interrupts only a small amount of the light falling on the concave mirror. Assume the eyepiece is a thin lens.  Find the transformation matrix M_VV' and the angular magnification m_q in terms of R and f_L.

Problem 5:

Consider the case of two positive thin lenses, L₁ and L₂, separated by 5 cm.  Their diameters are D₁ = 6 cm and D₂ = 4 cm and their focal length are f₁ = 9 cm and f₂ = 3 cm.  If an aperture with a hole 1 cm in diameter is located between them, 2 cm from L₂, find
(a)  the aperture stop,
(b)  the location and size of the exit pupil,
(c)  the location and size of the entrance pupil,
for for a very distant on-axis object.

Problem 6:

You want to build a Galilean telescope.  You have two convex lenses and two concave lenses available.  The larger lenses have focal lengths +80 cm and –80 cm respectively and the smaller lenses have focal lengths +20 cm and – 20 cm respectively.  Which lenses should you use and how far apart should you place them?  Explain!