Physics quiz question: focal length of a diverging lens

Physics 205B Quiz 2, spring semester 2019
Cuesta College, San Luis Obispo, CA

An object 1.0 cm in height located 8.0 cm in front of a diverging lens produces an upright image that is 0.75 cm in height. The focal length of this diverging lens is:
(A) –24 cm.
(B) –11 cm.
(C) –6.0 cm.
(D) –3.4 cm.

Correct answer (highlight to unhide): (A)

From the linear magnification equation:

m = h_i/h_o = –d_i/d_o,

the ratio between the image distance d_i and object distance d_o (8.0 cm) can be determined from the given image height h_i (+0.75 cm) and object height h_o (1.0 cm):

h_i/h_o = –d_i/d_o,

(+0.75 cm)/(1.0 cm) = –d_i/(8.0 cm),

–(8.0 cm)·(+0.75 cm)/(1.0 cm) = d_i = –6.0 cm.

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

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

(1/(8.0 cm)) + (1/(–6.0 cm)) = (1/f),

–0.04166666667... cm^–1 = (1/f),

–24 cm = f,

which is negative, as expected for a diverging lens.

(Response (B) is d_o·h_o/h_i; response (C) is d_i; response (D) is d_i·d_o/(d_o – d_i).)

Sections 30882, 30883
Exam code: quiz02BTLn
(A) : 17 students
(B) : 4 students
(C) : 7 students
(D) : 13 students

Success level: 41%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.90