## A screen is placed a distance dd to the right of an object. A converging lens with focal length ff is placed between the object and the scre

Question

A screen is placed a distance dd to the right of an object. A converging lens with focal length ff is placed between the object and the screen. In terms of f, what is the smallest value d can have for an image to be in focus on the screen?

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6 months 2021-08-09T05:20:28+00:00 1 Answers 18 views 0

2f

Explanation:

The formula for the object – image relationship of thin lens is given as;

1/s + 1/s’ = 1/f

Where;

s is object distance from lens

s’ is the image distance from the lens

f is the focal length of the lens

Total distance of the object and image from the lens is given as;

d = s + s’

We earlier said that; 1/s + 1/s’ = 1/f

Making s’ the subject, we have;

s’ = sf/(s – f)

Since d = s + s’

Thus;

d = s + (sf/(s – f))

Expanding this, we have;

d = s²/(s – f)

The derivative of this with respect to d gives;

d(d(s))/ds = (2s/(s – f)) – s²/(s – f)²

Equating to zero, we have;

(2s/(s – f)) – s²/(s – f)² = 0

(2s/(s – f)) = s²/(s – f)²

Thus;

2s = s²/(s – f)

s² = 2s(s – f)

s² = 2s² – 2sf

2s² – s² = 2sf

s² = 2sf

s = 2f