How large does a 5 mm insect appear when viewed with a system of two identical lenses of focal length 5 cm separated by a distance 12 cm if the insect is 10 cm from the first lens?
A)2.5 mm
B)5 mm
C)8.3 mm
D)10 mm
E)12.5 mm

Question

Quizplus · Accepted Answer

The magnification of the system can be calculated using the lens formula and magnification formula for each lens, and then multiplying the magnifications together. For the first lens, the object distance $u = -10$ cm (negative because we take the direction of incident light as positive), and the focal length $f = 5$ cm. Using the lens formula $\frac{1}{f} = \frac{1}{v} - \frac{1}{u}$, we can find the image distance $v$ for the first lens. This image acts as the object for the second lens, with its distance from the second lens being the difference between the separation of the lenses and the image distance from the first lens. Calculating through these steps, we find the overall magnification to be approximately 1.67, and thus, a 5 mm insect appears to be $5 \times 1.67 = 8.35$ mm, which rounds to 8.3 mm.

How Large Does a 5 Mm Insect Appear When Viewed