mirror problem?
The side-view mirror of an automobile has a radius of curvature of 11.5 cm. The mirror produces a virtual image one half the size of the object. How far is the object from the mirror? answer in units of cm.
The side-view mirror of an automobile has a radius of curvature of 11.5 cm. The mirror produces a virtual image one half the size of the object. How far is the object from the mirror? answer in units of cm.
Comments
ans: object is 5.75 cm. away from the mirror.
here's how:
1)since it is a convex MIRROR so focal length, f=R/2 where R is the radius of curvature. so f=11.5/2 = 5.75 cm.
2)Since the mirror produces a virtual image one half the size of the object, so magnification is 1/2 i.e 0.5 Also magnification for a MIRROR, m = -v/u, where v is the image distance from mirror and u is the object distance from mirror.
So. -v/u = 1/2
=>v = -u/2
Using MIRROR formula: 1/f = 1/u + 1/v
here f = 5.75, v = -u/2.
Put the values and u'll get the answer u=5.75 cm. (take care of sign i.e put value of v along with sign)
"closer that it appears"