Question

A thin double convex lens of focal length f, = + 15 centimeters is located at the origin of the x-axis, as shown above. An object of height 8 centimeters is placed 45 centimeters to the left of the lens.

a. On the figure below, draw a ray diagram to show the formation of the image by the lens. Clearly show principal rays.

b. Calculate (do not measure) each of the following.

i. The position of the image formed by the lens

ii. The size of the image formed by the lens

c. Describe briefly what would happen to the image formed by the lens if the top half of the lens were blocked so that no light could pass through.

A concave mirror with focal length f₂ = + 15 centimeters is placed at x = + 30 centimeters.

d. On the figure below, indicate the position of the image formed by the lens, and draw a ray diagram to show the formation of the image by the mirror. Clearly show principal rays.

Answer 1

(a)

(b) i) 1/f = 1/d_o + 1/d_i … 1/15 = 1/45 + 1/d_i … d_i = 22.5 cm.

ii) M = – d_i / d_o … M = –(22.5)/45 = –0.5 … M = h_i / h_o … –0.5 = h_i / 8 cm … h_i = – 4 cm

(c) When light from multiple locations pass through a given part of a lens to form an image, only a small portion of a lens is needed to form the image. The more of a lens, the more light rays that can be bent by it to each image location. This simply makes the image brighter. By covering half the lens, all of the incoming rays still bend all the same ways but there are less total rays being bent to given locations on the image so it is dimmer. This can easily be seen by looking at a lens that has only horizontal rays approaching it. All of these rays converge to the focal point; covering a portion of the lens still focuses the rays on the focal point, just less of them. this would cause the image to dim only.

(d)