(11%) Problem 1: Two lenses are mounted d = 31 cm apart on an optical bench. The

Question

(11%) Problem 1: Two lenses are mounted d = 31 cm apart on an optical bench. The focal length of the first lens is,h = 9.9 cm and that of the second lens isf 5.9 cm. An object of height ho-3.6 cm is placed at a distance of do-28 cm in front of the first lens 25% Part (a) Ignoring the second lens for now, at what distance, in centimeters, behind the first lens is the object's image formed by that lens? Grade Summary Deductions Potential 0% 100% sinO Submissions Attempts remaining: 7 (0% per attempt) detailed view 789 cotan0 asinO acos0 atanO acotan sinh0 cotanhO 0 END Degrees O Radians VO DELCLEAR Submit Hint I give up! Hints: 2% deduction per hint. Hints remaining: Feedback: 2% deduction per feedback. 25% Part (b) Calculate the magnification of that image, including its sign 25% Part (c) Which choice best describes that image? 25% Part (d) Now consider the two-lens system and the final image it forms, ie., the image created by the second lens. What is the distance, in centimeters, between the object and its final image?

Explanation / Answer

here,

for the first lens

the object distance , do1 = 28 cm

focal length , f1 = 9.9 cm

let the image distance be di1

using the lens formula

1/f1 = 1/di1 + 1/do1

1/9.9 = 1/di1 + 1/28

solving for di1

di1 = 15.3 cm

b)

magnifictaion , m1 = - di1/do1

m1 = - 15.3 /28 = - 0.54

d)

for the seccond lens

the object distance , do2 = d - di1

do2 = 15.7 cm

focal length , f2 = 5.9 cm

let the image distance be di2

using the lens formula

1/f2 = 1/di2 + 1/do2

1/5.9 = 1/di2 + 1/15.7

solving for di2

di2 = 9.45 cm

the distance between final image and object , s = do1 + d + di2

s= 68.5 cm

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