### Chapter 1: Light - Reflection and Refraction

Q
##### Light - Reflection and Reflection

Question:

An object 5.0 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.

Here, the given mirror convex.

Object Distance () = -20 cm

Radius of curvature () = +30 cm

Height of object () = 5 cm

Image Distance () = ?

Object distance () is taken negative as their distances from the pole of the mirror is measured opposite to the direction of the incident light.

Using the relation between and :

We get,

Now, using the mirror formula

The positive sign of indicates that the image is formed on the other side of the mirror at a distance of 8.57 cm. That is the image formed is virtual.

Now, magnification

Here, the magnification is positive and less than 1. The positive sign indicates that the image is erect and value less than 1 indicates that the size of the image is smaller than the object.

The positive sign of image height indicates that the image is erect.

Therefore, the image is formed at a distance of 0.428 cm on the other side of the mirror. The image formed is 2.14 cm tall and it is virtual, erect and smaller in size.

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