Physics quiz question: comparison of image distance with diverging lens focal length

Physics 205B Quiz 2, spring semester 2017
Cuesta College, San Luis Obispo, CA

An object is placed in front of a f = –20 cm diverging lens, which produces an upright image that is one-tenth the size of the object. The absolute value of the distance from the lens to the image is __________ 20 cm.
(A) less than.
(B) equal to.
(C) greater than.
(D) (Not enough information given.)

Correct answer (highlight to unhide): (A)

From the linear magnification equation:

m = h_i/h_o = –d_i/d_o,

the ratio between the object distance d_o and image distance d_i can be determined (where the linear magnification is +(1/10), as the image is diminished ("one-tenth the size of the object") and upright):

+(1/10) = –d_i/d_o,

d_o = –10·d_i.

Substituting this result for d_o into the thin lens equation will then obtain a value for the image distance d_i, as the focal length f is given:

(1/d_o) + (1/d_i) = (1/f),

(1/(–10·d_i)) + (1/d_i) = (1/f),

(9/(10·d_i)) = (1/f),

d_i = (9/10)·f = (9/10)·(–20 cm) = –18 cm,

which means that the image will be located to the left of the diverging lens (same side as the object), 2 cm closer than the diverging lens' left focal point.

Sections 30882, 30883
Exam code: quiz02J4sZ
(A) : 20 students
(B) : 3 students
(C) : 7 students
(D) : 0 students

Success level: 67%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.45