A concave spherical mirror has a radius of curvature of 10.0 cm . Part A) Calcul

ID: 1597582 • Letter: A

Question

A concave spherical mirror has a radius of curvature of 10.0 cm .

Part A) Calculate the size of the image formed by an 12.0 mm -tall object whose distance from the mirror is 20.0 cm .

Part B) Calculate the size of the image formed by an 12.0 mm -tall object whose distance from the mirror is 10.0 cm .

Part C) Calculate the size of the image formed by an 12.0 mm -tall object whose distance from the mirror is 2.50 cm .

Part D) Calculate the size of the image formed by an 12.0 mm -tall object whose distance from the mirror is 10.0 m .

We know that

focal length f = R / 2 = 5 cm

(a)

From the mirror formula,

1 / f = 1 / v + 1 / u

where u = distance of object from mirror

v = distance of image from mirror

1 / v = 1 / 5 - 1 / 20

v = 6.66 cm

magnification m = -v / u = hi / ho

-0.066 / 0.20 = hi / 0.012

hi = -0.00396 = -3.96 mm

(negetive sign represent that image is inverted.)

(b)

1 / v = 1 / 5 - 1/ 10

v = 10 cm

hi = -v*ho / u = -0.10*0.012 / 0.10

hi = -12 mm

(c)

1 / v = 1 / 5 - 1/ 2.5

v = -5 cm

hi = -(-0.05)*0.012 / 0.025

hi = 0.024 m = 24 mm

(d)

1 / v = 1 / 0.05 - 1 / 10

v = 0.050 m

hi = -0.050*0.012 / 10

hi = -0.060 mm

answer

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