Please help me with the following question. Make sure to explain how you got eac

Question

Please help me with the following question. Make sure to explain how you got each step so that I can learn. Please answer ALL PARTS of the question completely and correctly. Thanks in advance!

A concave mirror with a 40 cm radius of curvature is placed 10 cm in front of a candle 10 em tall (a) Find the location and size of the image. (b) Suppose you want to replace the mirror in part (a) with a i lens (n 1.4) and still get the sa image (in size and position) for the same object. Design such a lens (determine the radius of curvature of its two surfaces). Note that there are many correct answers to this question.

Explanation / Answer

a)

given

R = 40 cm

object distanace, u = 10 cm

object height, h = 10 cm

let v is the image distance.

focal length of the mirror, f = R/2 = 40/2 = 20 cm

Apply, 1/u + 1/v = 1/f

1/v = 1/f - 1/u

1/v = 1/20 - 1/10

v = -20 cm <<<<-----ANswer

here negative sign indicates the image is virtual. the image will be behind the mirror.

magnification, m = -v/u

= -(-20)/10

= 2

image height, h' = m*object height

= 2*10

= 20 cm <<<<-----ANswer

b) for the lens, u = 10 cm

v = 20 cm (for lens real image formed right side of lens)

let f is the focal length of the mirror.

apply, 1/f = 1/u + 1/v

1/f = 1/10 + 1/20

f = 6.67 cm

let R is the radius of cuvature of lens.

Apply, 1/f = (n-1)*(1/R + 1/R)

1/6.67 = (1.4 - 1)*(2/R)

R = 2*0.4*6.67

= 5.336 cm <<<<<--------ANswer

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