(a) A concave spherical mirror forms an inverted image 4.00 times larger than th

Question

(a) A concave spherical mirror forms an inverted image 4.00 times larger than the object. Assuming the distance between object and image is 0.700 m, find the focal length of the mirror.

(b) Suppose the mirror is convex. The distance between the image and the object is the same as in part (a), but the image is 0.500 the size of the object. Determine the focal length of the mirror.

A concave spherical mirror forms an inverted image 4.00 times larger than the object. Assuming the distance between object and image is 0.700 m, find the focal length of the mirror. The magnification gives a relationship between p and q. If you know the distance between the object and image, how do you determine the individual values of p and q? Suppose the mirror is convex. The distance between the image and the object is the same as in part (a), but the image is 0.500 the size of the object. Determine the focal length of the mirror.

Explanation / Answer

here,

a)

for concave mirror

- (di/do) = hi/ho

di = 4 * do ...(1)

and

di + do = 0.7 ...(2)

from (1) and (2)

di = 0.56 m

do = 0.14 m

using the lens formula

1/f = 1/di + 1/do

1/f =1/0.14 + 1/0.56

f = 0.11 m

the focal length is 0.11 m

b)

for convex mirror

- (di/do) = hi/ho

di = - 0.5 * do ...(1)

and

di + do = 0.7 ...(2)

from (1) and (2)

do = 1.4 m

di = - 0.7 m

using the lens formula

1/f = 1/di + 1/do

1/f = 1/1.4 - 1/0.7

f = - 1.4 m

the focal length is - 1.4 m

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