A spherical mirror forms an image of an arrow atx x2956 om. The mirror is represented in the
drawing as a plane atx -0. The tip of the object arrow is located at(xy) (x1y) (-114cm, 7.21 cm).
4y (xy) ") What is f, the focal length of the mirror? If the mirror is concave f is positive If the
mirror is conve f is negative Subm 2) What is y2, the y co-ordinate of the image of the tip of the
arrow? 3) The object arrow is now moved such that image distance doubles, i e, Ximage.new -
191 2 cm. What is yimagenew. the new y co-ordinate of the image of the tip of the arrow? 4) The
object arrow is now moved to x -x1new 35.4 cm. What is y2new. the new y co-ordinate of the
mage of the arrow? cm Submit
Solution
given
spherical mirro let focal length be f
then
for concave mirror the focal length is +ve ( given)
1. object position, u = -114 cm
v = -95.6 cm
mirror equation
1/v + 1/u = -1/f
-1/95.6 - 1/114 = -1/f
hence
f = 51.99618320 cm
hence the mirror is concave
2. magnification = -v/u = 0.838596491228

hence y coordinate of the tip of the image
y = -7.21*v/u = -6.046280701754 cm
3. v = -191.2 cm
f = 51.9961 cm
1/v + 1/u = -1/f
hence
u = -71.41792952 cm
m = -v/u = -2.6771988668380
new y coordinate y = -2.677198866838*(7.21) = -19.3026038299 cm
4. u = -35.4 cm
f = 51.9961 cm
hence
v = 110.909306403311621 cm
new y coordinate = -7.21*v/u = 22.589155343725 cm