Ray Optics and Optical Instruments

The driver sitting inside a parked car is watching vehicles approaching from behind with the help of his side view mirror, which is a convex mirror with radius of curvature R=2 m. Another car approaches him from behind with a uniform speed of 90 km/hr. When the car is at a distance of 24 m from him, the magnitude of the acceleration of the image of the car in the side view mirror is ' a '. The value of 100a is m/s2.

Answer

8

Solution

Convex mirror: f= R2=1 m, vO=25 m/s, u=-24 m; the image is virtual, behind the mirror (figure not to scale).

[figure]

Differentiate 1v+ 1u= 1f: vI=- f2(u-f)2 vO

Differentiate again (vO constant): a= 2f2vO2(u-f)3

|a|= 2 1 252253=0.08 m/s2

100a=8

Answer: 8