Correct Answer - Option 3 : The image is smaller in size by a factor of 0.20.
Concept:
Convex mirrors are used in the rear-view mirrors. Convex mirrors always form a virtual image.
Mirror Formula: The following formula is known as the mirror formula:
\(\frac{1}{f}=\frac{1}{u}+\frac{1}{v}\,\)
Where f = Focal length, v = Distance of the image from the mirror, u = Distance of the object from the mirror.
Also, R = 2f
R = Radius of curvature.
Magnification: In a concave mirror, the magnification is the ratio of the height of the image to the height of the object.
- When the image is real, the magnification will be negative because the real image is inverted.
- When the image is virtual, the magnification will be positive because the virtual image is erect.
\(m = \frac{-v}{u}\)
Where m = Magnificent
Calculation:
Given:
R = 4 m, u = -6 m
Since, R = 2f
f = 4 / 2
f = 2 m
Using \(\frac{1}{f}=\frac{1}{u}+\frac{1}{v}\)
\(\frac{1}{2}=\frac{1}{-6}+\frac{1}{v}\)
v = 1.5 m
Hence, the image will form at a distance of 1.5 m.
Magnification, \(m = \frac{-v}{u}\)
\(m = \frac{-1.5}{-6}\)
m = 0.25
Hence, the image is smaller by a factor of 0.50.
