Question

The radius of curvature of concave mirror is 50cm. where should an object be placed from the mirror so as form it's image infinity? justify your answer?​

Answer 1

Given, the radius of curvature of concave mirror = 50 cm

→ focal length of concave mirror = 25 cm

We know that if an object is kept at focus in front of a concave mirror, then the image is formed at infinity. Hence, the object should be placed 25 cm in front of the mirror.

Justification

Here,

v = ∞

We have to find u,

Applying mirror formula

1/v + 1/u = 1/f

→ 1/u = 1/f - 1/v

→ 1/u = 1/f - 1/∞

We know that, 1/∞ is extremely low value, and is approximately equal to zero.

→ 1/u = 1/f - 0

→ 1/u = 1/f

→ u = f

Hence, the object should be kept at focus to get an image at infinity.

Answer 2

Answer:

$\large\boxed{\sf{At \:focus, 25\: cm }}$.

Explanation:

Given that it's a concave mirror.

Radius of curvature, r = 50 cm.

• We know that, focal length is the half of the length of the radius of curvature .

Therefore, We have,

Focal length, f = 25 cm

• Also, we know that to get an image at infinity, an object must be placed at focus.

So, we have the Following cases,

• Object distance = u
• Image distance = v = $\infty$
• Focal length, f = 25 cm

Concept Map :-

Now, apply the mirror formula,

$\sf{ = > \frac{1}{v} + \frac{1}{u} = \frac{1}{f} }\\ \\ \sf{= > \frac{1}{\infty} + \frac{1}{u} = \frac{1}{25} }\\ \\ \sf{= > 0 + \frac{1}{u} = \frac{1}{25}} \\ \\ \sf{= > \frac{1}{u} = \frac{1}{25} }\\ \\ \sf{= > u = 25 \: cm}$

Hence, justified.