Question

a point of object is kept at a distance of 15 cm in front of a small concave mirror having radius of curvature 30cm . the image formed will be​

Answer 1

Answer:

$\boxed{\sf Image \ will \ be \ formed \ at \ infinity \ (v = \infty)}$

Given:

Object distance (u) = 15 cm

Radius of curvature (R) = 30 cm

To Find:

Image distance (v)

Explanation:

$\sf Focal \ length \ (f) = \frac{Radius \ of \ curvature \ (R)}{2}$

$\sf f = \frac{30}{2}$

$\sf f = 15 \: cm$

By using sign convention:

u = -15 cm

f = -15 cm

$\sf Mirror \ formula:$

$\sf \boxed{ \bold{\frac{1}{v} + \frac{1}{u} = \frac{1}{f}} }$

Substituting value of u and f in the mirror formula:

$\sf \implies \frac{1}{v} + \frac{1}{( - 15)} = \frac{1}{( - 15)}$

$\sf \implies \frac{1}{v} - \frac{1}{ 15} = - \frac{1}{ 15}$

$\sf \implies \frac{1}{v} = \frac{1}{15} - \frac{1}{15}$

$\sf \implies \frac{1}{v} = 0$

$\sf \implies v = \frac{1}{0}$

$\sf \implies v = \infty$

Answer 2

The image would form at Infinity

Explanation: As R= 30cm

F=R/2

   30/2

 = 15 cm

So focal length is 15cm

Now,

When the object is at focus image is at infinity.

So the image is formed at infinity.

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