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A movie camera with a (single) lens of focal length 75mmtakesa picture ofa person standing 27maway. If the person is180cmtall, what is the height of the image on the film?

Short Answer

Expert verified

The height of the image on the film is 0.5cm.

Step by step solution

01

Listing the given quantities

Focal length

f=75mm=7.5cm

Object distance

p=27m=2700cm

Height of the personH=180cm

02

Understanding the concepts of optics

The focal length and the object distance is given in the problem. By using the lens equation, we can find the image distance. Using the relation between the magnification, the image distance and the object distance, we can find the magnification. Using the height of the object given in the problem, we can find the height of the image.

Formula:

1f=1i+1pm=-ipm=Imageheight(h')Originalheight(H)

03

Calculations of the height of the image on the film

We have,

1f=1i+1p

Rearranging for,

1i=1f-1pi=11f-1p=117.5-12700=7.5cm

We have,

m=-ipm=Imageheighth'OriginalheightH-ip=Imageheighth'OriginalheightH

Imageheighth'=-ip×OriginalheightH=-7.52700×180=0.5cm

The height of the image on the film is =0.5cm.

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