1. In the diagram below, an image of an L = 5.00 cm long arrow is formed on the transmission side of a converging lens of focal length f = 20.0 cm. The head of the arrow is 60.0 cm from the lens. What is the longitudinal magnification M = L’/L of the image?
   

2. Consider a positive lens of focal length f.
   

   (a) Show that D = s²/(s-f), where D is the distance between the object and the image and s is the distance the object is from the lens as shown in the diagram below.
   

   (b) Find the value of s for which D is a minimum. (Recall from Math 1120, that finding a minimum or maximum involves taking a derivative.)

   (c) What is the minimum possible D in terms of f?

   

3. The prism shown below has an index of refraction of 1.60. It is immersed in water which has an index of 1.33.
   

   (a) Find the minimum angle θ for which there will be total internal reflection at surface AB.

   (b) Trace the ray all the way through and find the angle to the normal in the water that it makes it leaves the prism on side CB.

   

4. A certain person has a farpoint of 100 cm and a nearpoint of 15 cm.
   (a) Find the focal length of the contact lenses needed.
   (b) Wearing the contact lenses will affect how close an object can be brought to the eye, i.e. there will be a new nearpoint with the lenses on. Find that new nearpoint. Assume that the eye is 24 mm across.
   (c) Nearsighted people often remove their glasses if they need to do fine work such as threading a needle. Use your answer from part (b) to explain why.
   

5. A fish is 15.0 cm below the surface of the water in a fishtank. The bottom of the fishtank, 20.0 cm below the fish, is a mirror. To an observer looking almost straight down, where does the image of the fish in the mirror appear to be?
   
   

6. In the diagram below, light from the object at P passes through the lens from the left, is reflected off the spherical mirror and then back through the lens to the eye. This problem is similar to the multiple lens problems we have done before with one important exception, for the light coming back through the lens the righthand side of the lens is now the incident side. This must be taken into account when you use the sign convention for the last leg of the light path. The converging lens has focal length f₁ = 20.0 cm. The concave mirror has radius R = 12.0 cm. The lens and the centre of the mirror are 40.0 cm apart. An object is placed 80.0 cm from the lens at point P.
   (a) Where is the image formed by the first passage through the lens. Characterize this image.
   (b) Where is the image formed by the reflection off the mirror. Characterize this image.
   (c) Where is the image formed by the second, return, passage through the lens. Characterize this image.
   (d) Compared to the actual object, characterize the final image (i.e. what is the overall orientation and magnification?).
   

7. The accompanying sheet of graph paper shows an object and two lenses. The focal points of the positive lens are denoted by F+ and of the negative lens by F-. Use the ray technique to find the image. Is the image real or virtual? Compared to the object at O, is the final image erect or inverted? Include an estimate of the magnification.
   

Reflection, Refraction, & Polarization:

θi = θr	n = c/v	n1sinθ1 = n2sinθ2
sinθcritical= n2/n1	I = I0cos2θ	tanθp = nlower/nupper

Mirrors & Lenses:

f = ½R	1/o + 1/i = 1/f	1/fcombined = 1/f1 + 1/f2
dapparent = -n2dactual/n1	M = -i/o

Mirrors		Lenses
o	= + object in front of mirror	o	= + object on incident side
o	= - object is behind mirror	o	= - object on transmission side
i	= - image is behind mirror	i	= + image is on transmission side
i	= + image is in front of mirror	i	= - image on incident side side
f,R	= + concave side is mirror	f	= + converging lens, centre is thicker
f,R	= - convex side is mirror	f	= - diverging lens, centre is thin

Optical Instruments:

Msimple = θ/θo = xNP/f	f-number = f/D
Lfilm µ ID2t	MMicroscope = -(L/fobjective)(xNP/feyepiece)
MTelescope = -fobjective/feyepiece

Questions? mike.coombes@kpu.ca