Question

a 20 cm object is placed on the principal axis of a concave mirror at a distance 12 cm from the pole .if the image is inverted real and 5 cm high find the location of image and the focal length of the mirror?

Answer 1

Answer on Question #62129 - Physics - Optics

Question:

A 20 cm object is placed on the principal axis of a concave mirror at a distance 12 cm from the pole. If the image is inverted real and 5 cm high find the location of image and the focal length of the mirror?

Solution:

Let $|AB| = H$, $|A'B'| = h$, $|AP| = D$, $|A'P| = d$, focal length $f = |FP|$.

$$H = 20 \text{ cm}, h = 5 \text{ cm}, D = 12 \text{ cm}$$

Magnification for this spherical mirror $M = \frac{h}{H}$.

On the other hand $M = \frac{d}{D}$ and we can write that $\frac{h}{H} = \frac{d}{D}$ and therefore $d = D \times \frac{h}{H}$.

So, $d = 12 \times \frac{5}{20} = 3$ cm.

The formula for spherical mirror looks like this: $\frac{1}{f} = \frac{1}{D} + \frac{1}{d}$. So we can derive that $f = \frac{1}{\frac{1}{D} + \frac{1}{d}}$.

Thus, $f = \frac{1}{\frac{1}{12} + \frac{1}{3}} = 2.4$ cm.

Answer:

The distance of image from the pole is $3 \text{ cm}$.

Focal length of the mirror is $2.4 \text{ cm}$.

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