Question

A butterfly at eye level is 20cm in front of a plane mirror. You are behind the butterfly, 50cm from the mirror. What is the distance between your eye and the image of the butterfly in the mirror?

Answer 1

Hint:In case of plane mirrors, distance of the object and the image from the mirror is the same, i.e the image is the same distance behind the mirror as in front of the mirror. For example if we stand a distance of 5 meters from a plane mirror, we must look at a location 5 meters behind the mirror in order to view our image.

Complete Step by Step Answer:
An image of an object formed in a plane mirror is of the same size as the object and is located behind the mirror at the same distance. The image is formed by using the laws of reflection. According to the law of reflection, when a ray of light reflects a surface then, the angle of incidence is equal to the angle of reflection. The incident ray, reflected ray and the normal at the point of the incidence all lie in the same plane.

${\theta _1}$ =angle of incidence
${\theta _2}$ =angle of reflection
For a smooth surface the angle of incidence ${\theta _1}$ is equal to the angle of reflection ${\theta _2}$ as measured with reference to the normal line perpendicular to the surface.Butterfly is positioned at a distance of 20cmfrom the observer’s eye level in front of a plane mirror. The image distance is equal to the object distance. The image distance will be 20cm.The distance between observer’s and the mirror is 50cm. We can calculate the distance between eye and image of butterflies. Firstly, to make a sketch, simply draw a plane mirror then an observer standing 50cm in front of it and label a butterfly 20cm in front of the mirror.

Whatever distance you are from the mirror is the distance the reflection appears to be on the other side, so the distance into the mirror of the reflection of the butterfly is 20cm. Adding the distance of you from the mirror is
$
d = 50 + 20 \\
\therefore d = 70cm $

Hence, the distance between your eye and the image of the butterfly in the mirror is $70\,cm$.

Note: In the case of plane mirrors, the image is called a virtual image. Virtual images are formed in locations where light does not reach or we can say that Light does not actually pass through the location on the other side of the mirror. Images only appear to an observer as though the light is coming from this location. Whenever a plane mirror brings an image that is virtual, behind the mirror the image will be located where light does not really come from. On the other side real images are formed by curved mirrors. Such images are created on the same side of the mirror as the object and light passes through the actual image location.