Question

A concave mirror forms an image of an object magnification is 3. when the object is moved 10 cm towards the mirror, the magnification is 5. find its focal length .​

Answer 1

Answer:

For mirror u=

m

f(m−1)

In first case, u=

−4

f(−4−1)

In the second case, u+3=

−3

f(−3−1)

On solving, we get f=36cm

Answer 2

${\huge{\boxed{\mathcal{\red{Answer}}}}}$

18.75

${\huge{\boxed{\mathcal{\red{Explanation}}}}}$

The image of an objects is said to be magnified when height of image is greater than height of object.

Magnification is the ratio of image distance to object distance. Mathematically it is represented by following equation :

$m = \frac{v}{u}$

In this equation :

• m = magnification
• v = image distance
• u = object distance.

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Now in the first case m = 3 , thus we can say

$3 = \frac{v}{u}$

In the second case object is moved 10cm towards the mirror this means that the object distance has been decreased by 10cm. It is given in this case magnification is 5, thus we can say:

$5 = \frac{v}{u - 10}$

From the first equation we can say

$v = 3u$

Substituting value of v in equation 2 we get:

$5 = \frac{3u}{u - 10}$

$5(u - 10) = 3u$

$5u - 50 = 3u$

$- 50 = - 2u$

$u = 25cm$

Now substituting value of u in equation 1 we get:

$v = 3 \times 25$

$v = 75cm$

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Now according to mirror formula :

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

$f = \frac{uv}{u + v}$

After inputting values in this equation we get:

$f = \frac{25 \times 75}{25 + 75}$

$f = \frac{1875}{100}$

$f = 18.75$

Thus focal length of mirror is 18.75 cm.

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BY SCIVIBHANSHU

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