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Chapter 31: Problem 48

How far apart are the object and image produced by a converging lens with 35 -cm focal length when the object is (a) \(40 \mathrm{cm}\) and (b) \(30 \mathrm{cm}\) from the lens?

Short Answer

Expert verified
The image distance 'v' for an object distance of 40 cm is approximately 140 cm. For an object distance of 30 cm, the image distance 'v' is approximately 52.5 cm.

Step by step solution

01

Identify Given Information

Given is a converging lens with a focal length of 35 cm and two different distances of the object; first of 40 cm and secondly of 30 cm. The aim is to calculate the image distance.
02

Apply the Lens Formula for Object Distance of 40 cm

Insert the values of object distance and focal length into the lens formula. Object distance, 'u', is -40 cm (negative since it's conventionally on the opposite side of the lens); focal length, 'f', is 35 cm. Solve this for the image distance, 'v'. The equation becomes \(1/35 = 1/v 鈥� 1/(-40)\).
03

Solve for Image Distance (40 cm Object Distance)

Solving this equation will provide the image distance for the object distance of 40 cm. Subtracting \(1/(-40)\) from both sides gives the equation for image distance 'v' as \(1/v = 1/35 +1/40\). On solving for 'v', by taking the invert of both sides, this will give the image distance for this case.
04

Apply the Lens Formula for Object Distance of 30 cm

In a similar manner, insert the second given object distance and focal length into the lens formula for when 'u' is -30 cm. This gives the equation \(1/35 = 1/v 鈥� 1/(-30)\).
05

Solve for Image Distance (30 cm Object Distance)

By the same process as in step 2, solve this equation for the image distance for the object distance of 30 cm. Subtracting \(1/(-30)\) from both sides gives the equation for 'v' as \(1/v = 1/35 +1/30\). On solving by taking the invert of both sides, you obtain the image distance for this case.

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