A 4.0-cm object is placed 30.0 cm from a converging lens that has a focal length of 10.0 cm as shown in the diagram.
Note: The diagram is not drawn to scale.

-Determine the height and orientation of the image.
A)2 cm and upright
B)1 cm and inverted
C)2 cm and inverted
D)8 cm and upright
E)8 cm and inverted

Question

A 4.0-cm object is placed 30.0 cm from a converging lens that has a focal length of 10.0 cm as shown in the diagram.
Note: The diagram is not drawn to scale.
 
-Determine the height and orientation of the image.
A)2 cm and upright 
B)1 cm and inverted 
C)2 cm and inverted 
D)8 cm and upright 
E)8 cm and inverted

Quizplus · Accepted Answer

Using the thin lens equation:

1/f = 1/do + 1/di

where f is the focal length, do is the object distance, and di is the image distance.

Plugging in the given values:

1/10 = 1/30 + 1/di

Solving for di:

di = 15 cm

Using the magnification equation:

M = hi/ho = -di/do

where hi is the image height and ho is the object height.

Plugging in the given values:

M = hi/ho = -15/30 = -1/2

Since the magnification is negative, the image is inverted. The absolute value of the magnification represents the ratio of the image height to the object height:

|M| = |hi/ho| = 1/2

Therefore, hi = 1/2 * ho = 1/2 * 4 cm = 2 cm

So the answer is choice C: 2 cm and inverted.

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