Chapter 29, Problem 51A

A spider hangs by a strand of silk at eye level 20 cm in front of a plane mirror. You are behind the spider, 50 cm from the mirror. Show that the distance between your eye and the image of the spider in the mirror is 70 cm.

To determine

To show: the distance between an eye and the image of the spider in the mirror is $70cm$

Explanation of Solution

Introduction: 

The distance between the object and the mirror is known as a distant object and it is positive. If the same object behind the mirror appears to be at the same distance and at the same height and it is virtual and the image distance is negative.  

Explanation: 

The distance of positive and negative image shows the total distance between the eye and the image behind the mirror. For example, an object in front of the mirror is at a distance of $2m$ and the image of the object behind the mirror is at the same distance of $2m.$

Since an object in front of the mirror is equal to the distance of the image behind the mirror the spider is at $20cm$ behind the mirror and the person's eye is at $50cm$ in front of the mirror, the total distance between the eye and the image of spider is $70cm$

Hence the distance between the eye and the image of spider is $20+50=70cm$

Conclusion: 

The distance between the eye and the image of the spider is $20+50=70cm$