Question

calculate the focal length a concave mirror which produces magnification - ½ when object is placed at 30cm infront of it​

Answer 1

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Wr have been given that :-

• Magnification of object = -1/2
• Object distance = 30cm
• Image distance = v = ?
• Focal length of mirror = ?

Now, we know that magnification of a image is the ratio of image distance to object distance. Defined by the expression :-

$\maltese \: m = \frac{ - v}{u}$

After inputting the values for this case we get :-

$\maltese \: \frac{ - 1}{2} = \frac{ - v}{30}$

$\maltese \: - 30 = - 2v$

$\maltese \: 30 = 2v$

$\maltese \: v = \frac{30}{2}$

$\maltese \: v = \cancel \frac{30}{2}$

$\maltese \: v = 15cm$

Therefore in this case we get the image distance to be 15cm.

Now, we know according to mirror formula :-

$\maltese \: \frac{1}{f} = \frac{1}{v} + \frac{1}{u}$

$\maltese \: f = \frac{uv}{v - u}$

After inputting the values for this case we get :-

$f = \frac{ - 30 \times 15}{30 - 15}$

$\mapsto \: f = \frac{ - 450}{15}$

$\mapsto \: f = 30cm$

Therefore the focal length of given concave mirror is 30cm.

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BY SCIVIBHANSHU

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