Question

You are trying to study the flight of humming birds. For this, you make a setup such that you look through a camera at the image of a humming tree in a plane mirror. The camera is 4.30 m in front of the mirror. The bird is at camera level, 5.00 m to your right and 3.30 m from the mirror. How far will you see the image of the bird in the mirror? Refer to the diagram below. (Also, assume your eye is very very close to the camera)

• A. 3.30 m
• B. 7.60 m
• C. 4.60 m
• D. 9.10 m

Answer 1

The correct option is D 9.10 m

Image distance = object distance for a plane mirror, so, as the humming bird is 3.3 m in front of the mirror, the image is 3.3 m behind the mirror. Now, the distance between the mirror and the camera, along the direction perpendicular to the mirror is 4.3 m. (That is the physics translation of the English 'The camera is 4.3 m in front of the mirror'!). So, the distance from the image to the camera along this direction (English=in front of the mirror, again) is 4.3 m + 3.3 m = 7.6 m.
Also, it is given that the bird is 5 m to the right of the camera, so, the image will also be 5 m to the right (physics = 5 m along the mirror's direction). Hence, the image is 5 m along the mirrors direction, and 7.6 m along the direction perpendicular to it. (English = 5 m to the right and 7.6 m in front of the camera!). Using Pythagoras theorem, the total distance $=\sqrt{{7.6}^2+5^2}=9.1m.$