A convex mirror used on a bus has a focal length of 200 cm. If scooter is located at 100 cm. From this mirror find the position , nature and magnification of the image formed in the mirror
Answers
Answer:
➡ Hence, the position of the image = 66.667 cm
➡ Nature = Virtual, Erect, behind the mirror and diminished.
➡ Hence, the magnification of the image formed = 0.6667
Explanation:
Given :
Mirror = Convex (Diverging)
➡ Focal length of the mirror, f = 200cm
➡ Position of object, u = - 100cm
Let the position of image be 'v'.
By using mirror formula, we get,
1 / f = 1 / u + 1 / v
By applying the values, we get,
➡ 1 / 200 = (-1) / 100 + 1 / v
➡ 1 / v = 1 / 200 - (-1) / 100
➡ 1 / v = 1 / 200 + 1 / 100
➡ 1 / v = (1 + 2) / 200
➡ 1 / v = 3 / 200
➡ v = 200 / 3 = 66.667 cm
Hence, the position of the image = 66.667 cm
Since, the mirror is Convex, so the image is formed at 66.6cm behind the mirror and it is virtual image.
Nature = Virtual, Erect, behind the mirror and diminished.
We know that,
Magnification, m = -v / u
m = -v/u
m = -(66.677) / (-100) = 0.6667
Hence, the magnification of the image formed = 0.6667
∴ The image is erect and smaller in size by a factor of 0.66