Name: Power of Lenses
Uploaded: 2019-07-19
Duration: 4 min 48 s
Description: What is the difference between different eyeglasses? The power of a lens is the measure of how well the lens converges or diverges light rays. Let’s visualise.

Question

An object

5 cm

in length is placed at a distance of

20 cm

in front of a convex mirror of radius of curvature

30 cm

. Find the position of the image, its nature, and size.

Accepted Answer

Given: Radius of curvature, $R = 30 cm$

Object distance, $u = - 20 cm$

Height of object, $h = 5.0 cm$

Height of the image, $h^{,}$ = ?
We have, the focal length of a convex mirror $f = \frac{R}{2} = \frac{30}{2} = 15 cm$

Using mirror formula, $\frac{1}{f} = \frac{1}{v} + \frac{1}{u} \Rightarrow \frac{1}{v} = \frac{1}{f} - \frac{1}{u} \Rightarrow \frac{1}{v} = \frac{1}{15} - \frac{1}{- 20} \Rightarrow v = 8.57 cm$

From this, it is clear that the image is formed at $8.57 cm$ away back of the mirror and it is a virtual image.

Magnification, $m = \frac{h^{,}}{h} = - \frac{v}{u} = - \frac{8.57}{- 20} = 0.43$
Since magnification is positive, the image will be erect.

Height of image, $h' = m \times h = 0.43 \times 5 = 2.15 cm$

Therefore, the image formed will be virtual, erect and diminished.

An object $5 cm$ in length is placed at a distance of $20 cm$ in front of a convex mirror of radius of curvature $30 cm$ . Find the position of the image, its nature, and size.

Important Questions on Light - Reflection and Refraction

Learn and Prepare for any exam you want !

An object 5 cm in length is placed at a distance of 20 cm in front of a convex mirror of radius of curvature 30 cm. Find the position of the image, its nature, and size.

Important Questions on Light - Reflection and Refraction

Learn and Prepare for any exam you want !

An object $5 cm$ in length is placed at a distance of $20 cm$ in front of a convex mirror of radius of curvature $30 cm$ . Find the position of the image, its nature, and size.