Question

A 4.5 cm needle is placed 12 cm away from a convex mirror of focal length of 15 cm . Give the location and magnification of the image . Describe what happens as the needle is moved farther from mirror.​

Answer 1

A 4.5 cm needle is placed 12 cm away from a convex mirror of focal length of 15 cm . Give the location and magnification of the image . Describe what happens as the needle is moved farther from mirror.

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Height of needle ..h..= 4.5 cm

Object distance..u... = 12 cm

Focal length of convex mirror... f

... = 15 cm

1/f= 1/u + 1/v

1/15 + 1/12 = 4+5/60 = 9/60

v = 60/9 = 6.7 cm

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Answer 2

Distance of object from the mirror ( u ) = 12 cm .

Distance of image from the mirror ( v ) = ?

Focal length ( f ) = 15 cm .

Lens formula

$\frac{1}{f}=\frac{1}{v}+\frac{1}{u}\\\\\implies \frac{1}{15}=\frac{1}{v}-\frac{1}{12}\\\\\implies \frac{1}{v}=\frac{1}{15}+\frac{1}{12}\\\\\implies \frac{1}{v}=\frac{4+5}{60}\\\\\implies v=\frac{60}{9}\\\\\implies v=\frac{20}{3}\\\\\implies v=6.6666 cm$

As we move farther the  image will be diminished as the lens is convex lens .

ANSWER :

v = 6.67 cm .

Explanation :

In a convex lens :

u is always negative .

f is always positive .

Hence the lens formula gets altered a bit and we can find the distance by using the magnification formula also .

We know that the convex lens has negative magnification and hence it always diminishes the image .

Thus the nature will be diminished .