Question

Calculate the distance and magnification of an object placed 20cm from a converging lens

60cm and 0.3 times the size of object
20cm and 0.3 times the size of object
60cm and 3 times the size of object
80cm and 3 times the size of object

Answer 1

Answer on Question #46398, Physics, Optics

Question

Calculate the distance and magnification of an object placed 20cm from a converging lens

- 60cm and 0.3 times the size of object

- 20cm and 0.3 times the size of object

- 60cm and 3 times the size of object

- 80cm and 3 times the size of object

Solution

The lens equation expresses the quantitative relationship between the object distance $(d_o)$, the image distance $(d_i)$, and the focal length (f). The equation is stated as follows:

$$\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}$$

The magnification equation relates the ratio of the image distance and object distance to the ratio of the image height $(h_i)$ and object height $(h_o)$. The magnification equation is stated as follows:

$$M = \frac{h_i}{h_o} = -\frac{d_i}{d_o}$$

These two equations can be combined to yield information about the image distance and image height if the object distance, object height, and focal length are known.

Thus, when

- $d_i = 60$ cm, then $M = -\frac{60}{20} = -3$, so the image is inverted and is 3 times of original height.

- $d_i = 20$ cm, then $M = -\frac{20}{20} = -1$, so the image is inverted and has original height.

- $d_i = 80$ cm, then $M = -\frac{80}{20} = -4$, so the image is inverted and is 4 times of original height.

Thus, the correct variant of answer is 60cm and 3 times the size of object

Answer: 60cm and 3 times the size of object

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