Thin lenses: An optical system comprises in turn, from left to right: an observer, a lens of focal length +30 cm, an erect object 20 mm high, and a convex mirror of radius 80 cm. The object is between the lens and the mirror, 20 cm from the lens and 50 cm from the mirror. The observer views the image that is formed first by reflection and then by refraction. What is the position of the final image, measured from the mirror?

Question

Quizplus · Accepted Answer

First, we need to find the position of the image formed by the convex mirror. Using the mirror equation:

1/f = 1/p + 1/q

Where f is the focal length of the mirror, p is the object distance, and q is the image distance. We know f = 80 cm, p = 50 cm, so:

1/80 = 1/50 + 1/q

Solving for q, we get q = -160 cm. The negative sign tells us that the image is virtual (behind the mirror) and upright.

Next, we can use the thin lens equation to find the position of the final image formed by the lens:

1/f = 1/p' + 1/q'

Where f is the focal length of the lens, p' is the object distance (which is now the image distance from the mirror), and q' is the image distance from the lens. We know f = 30 cm, p' = -q = 160 cm, so:

1/30 = 1/160 + 1/q'

Solving for q', we get q' = 34.3 cm. This is the position of the final image as seen by the observer.

To find the position of the final image measured from the mirror, we need to subtract the distance between the lens and the mirror (20 cm) from the image distance:

34.3 - 20 = 14.3 cm

Therefore, the answer is choice C, 114 cm.

Thin Lenses: an Optical System Comprises in Turn, from Left