Question

A convex mirror forms a virtual image half the size the objects. Assuming the distance between the image and object is 20 cm determine the radius of curvature of the mirror

Answer 1

Answer:

The mirror equation is a standard equation to relate the object and image distance with the focal length of the spherical mirror. The expression of the mirror equation is as follows;

Answer 2

A convex mirror forms a virtual image half the size of the objects. Assuming the distance between the image and object is 20 cm, the radius of the curvature of the mirror is 26.66 cm.

Given: The mirror is convex in shape and it forms a virtual image. The virtual image is half in size of the object. The distance between the image and the object is 20 cm.  

To Find: We have to find the radius of curvature of the convex mirror.

Solution:  Let, the height of the image is h₁ and the height of the object is h₂.

then magnification(m) of the mirror is,

$m = \frac{h_{1} }{h_{2} } = \frac{1}{2}$

let, the distance of the image from the mirror is v and the distance of the object from the mirror is u.

then we can express magnification as,

$\frac{-v}{u} = \frac{1}{2}\\ = > u = -2v$

In the above equation, the negative sign denotes the direction of the distance from the mirror.

The distance between the object and the image is 20 cm.

Then,

$u + v = 20\\= > 2v + v = 20\\= > v = 6.66$

In the equation above we haven't taken the negative sign in the calculation as we are taking only the value of u, not its direction from the mirror.

As we know u = -2v, we can say that u = -13.33cm

Let, the focus of the mirror is f.

Now, from the mirror equation,

$\frac{1}{v} + \frac{1}{u} = \frac{1}{f}\\ = > \frac{1}{6.66} - \frac{1}{13.33} = \frac{1}{f}\\= > \frac{6.66}{88.778} = \frac{1}{f}\\ = > f = 13.33$

So, the focal length of the mirror is 13.33 cm.

We know, the radius of curvature = 2f

Hence, the radius of curvature is found to be 26.66cm.

#SPJ2