Question

The plane-convex lens shown above has a focal length f of 20 centimeters in air. An object is placed 60 centimeters (3f) from this lens.

a. State whether the image is real or virtual.

b. Determine the distance from the lens to the image.

c. Determine the magnification of this image (ratio of image size to object size).

d. The object, initially at a distance 3f from the lens, is moved toward the lens. On the axes below, sketch the image distance as the object distance varies from 3f to zero.

e. State whether the focal length of the lens would increase, decrease, or remain the same if the index of refraction of the lens were increased. Explain your reasoning.

Answer 1

(a) When placed outside of f, converging lenses make real images, this can be shown with the math below.

(b) 1/f = 1/d_o + 1/d_i … 1/20 = 1/60 + 1/d_i … d_i = 30 cm.

(c) M = – d_i / d_o … M = –(30)/60 = –0.5

(d) Based on the lens equation in b virtual images (–) for do less than f. undefined at f, approaches infinity. di approaches f as do becomes large.→

(e) Based on n_i sin θ_i = n_r sin θ_r, snells law, by increasing the index of refraction, the refraction angle increased (more bending) which would move the focal point closer. This can be seen by looking at horizontal rays that bend through the focal point. These rays would bend more making the focal point closer (smaller f)