Question

A thin convex lens A of focal length f_A  = 10 cm is positioned on an x-axis as shown above. An object of height 5 cm, represented by the arrow, is positioned 15 cm to the left of lens A.

(a) On the figure above, draw necessary rays and sketch the image produced by lens A.

(b) Calculate the location of the image produced by lens A.

(c) Calculate the height of the image produced by lens A.

A second thin convex lens B of focal length f_B = 10 cm is now positioned 10 cm to the right of lens A, as shown above.

(d) Determine the location on the x-axis given above of the final image produced by the combination of lenses.

(e) Check the appropriate spaces below to indicate the characteristics of the final image produced by the combination of lenses.

____ inverted ____ larger than the original object

____ upright ____ smaller than the original object

Explain your answers.

Answer 1

(a)

(b) 1/f = 1/d_o + 1/d_i … 1/10 = 1/15 + 1/d_i … d_i = 30 cm.

(c) M = – d_i / d_o … M = (–30)/15 = – 2 … M = h_i / h_o … –2 = h_i / 5 cm … h_i = – 10 cm

(d)

Mathematically: The image location for the first lens that we found in part ‘b’ (30cm from lens A), becomes the object for the second lens. Since this ‘pre–image’ would form on the other side of lens B, in relation to where the light originated from, and it is to be used as the object distance, the only way to account for this is to make the object distance do negative for the second lens (this is one of the few times this is possible). Based on the location of the second lens, the do for that lens equation would be – 20 cm. Solving that equation results in di = + 6.7 cm (measured from lens B) which means it is located at 16.7 cm on the scale shown. 

(e) This image is smaller, real, inverted.