A person\'s face is 30.0 cm in front of a concave shaving mirror. (a) If the ima

Question

A person's face is 30.0 cm in front of a concave shaving mirror. (a) If the image is an upright image 2.50 times as large as the object, what is t he mirror's focal length? (b) If instead the mirror was two lensesone converging with focal length 20.0 cm and and one divergine with facal length -10.0 cm are placed 25.0 cm apart. An object is placed 60.0 cm in front of the converging lens. Determine t he position and the magnification of the final image formed. Suppose a prism has an apex angle of 60.0 degree and index of refraction n = 1.60, what angle of incidence is required for a ray entering the left side of the prism if it is to exit the right side with an identical angle? Show supporting mathematics.

Explanation / Answer

12)

(a)

object distance s = 30 cm

magnification m = -s'/s = 2.5

image distance s' = -2.5*s = -2.5*30 = -75 cm

from mirror equation

1/s + 1/s' = 1/f

1/30 - 1/75 = 1/f

f = 50 cm <<<<-----answer

(b)

for converging lens

object distance s1 = 60 cm

focal length f1 = 20 cm

1/s1 + 1/s1' = 1/f1

1/60 + 1/s1' = 1/20

s1' = 30 cm

magnification m1 = -s1'/s1 = -30/60 = -0.5

for diverging lens

object distance s2 = 25 - 30 = -5 cm

focal length f2 = -10 cm

1/s2 + 1/s2' = 1/f2

-1/5 + 1/s2' = -1/10

s2' = 10 cm

image is 10 cm to the right of diverging lens <<<-----answer

m2 = -s2'/s2 = -10/-5 = 2

total magnificatio M = m1*m2 = 1 <<<-----answer

+++++++++++++

from prism formula

u = sini/sin(A/2)

A = apex angle

1.6 = sini/sin30

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