Physics quiz question: object at diverging lens focal point

Physics 205B Quiz 2, spring semester 2013
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 23.63

Placing an object 15 cm to the left of a f = –15 cm diverging lens will produce a(n) __________ image.
(A) diminished, real.
(B) enlarged, real.
(C) diminished, virtual.
(D) enlarged, virtual.
(E) (No image would be produced.)

Correct answer (highlight to unhide): (C)

Solving for the location of the image d_i:

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

(1/d_i) = (1/f) – (1/d_o),

(1/d_i) = (1/(–15 cm)) – (1/(+15 cm)) = –(2/(15 cm)),

d_i = –(15 cm)/2 = –7.5 cm,

where the negative sign by convention makes this a virtual image located to the left side of the lens (the same side of the lens as the original object). The linear magnification m is given by:

m = h_i/h_o = –d_i/d_o = –(– 7.5 cm)/(15 cm) = +0.50,

which means that this virtual image is diminished, being one-half of the size of the original object (and will be upright, due to the positive sign).

Section 30882
Exam code: quiz02hYp0
(A) : 2 students
(B) : 1 student
(C) : 13 students
(D) : 8 students
(E) : 9 students

Success level: 39%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.56