Worksheet: Thin Lenses

In this worksheet, we will practice applying the thin lens formula to lenses of different radii of curvature and refractive indices to find their foci.

Q1:

A camera with a 100 mm-focal length lens is used to photograph the Sun. What is the height of the Sun’s image at the camera’s photosensor? Use a value of 1 . 4 0 × 1 0 km for the diameter of the Sun and use a value of 1 . 5 0 × 1 0 km for the distance to the Sun.

Q2:

Suppose your 50.0 mm-focal length camera lens is 51.0 mm away from the film in the camera.

How far away is an object that is in focus?

What is the height of the object if its image is 2.00 cm high?

Q3:

A slide projector uses a 1 . 0 0 × 1 0 mm-focal length lens to project images onto a screen.

How far away is the screen if a slide is placed 103 mm from the lens and produces a sharp image on the screen?

If the dimensions of the slide are 24.0 cm by 36.0 mm, what are the dimensions of the image on the screen?

  • A 9 0 . 0 × 9 0 . 0 c m c m
  • B 1 2 0 × 1 2 0 c m c m
  • C 1 6 2 × 1 6 2 c m c m
  • D 6 4 . 8 × 6 4 . 8 c m c m
  • E 3 6 . 0 × 3 6 . 0 c m c m

Q4:

A 10.0 cm-focal length lens produces a magnification of + 3 . 0 0 for a book held 7.50 cm from it.

Find the magnification for the book when it is held 8.50 cm from the magnifier.

Find the magnification for the book when it is held 9.50 cm from the magnifier.

Q5:

A camera with a 50.0-mm focal length lens is being used to photograph a person standing 3.00 m away.

How far from the camera’s lens is its photosensor?

What is the maximum height of a person whose image can be formed onto a 36.0 mm high section of photosensor using this camera at this distance?

Q6:

An object has a height of 3.0 cm. The object is placed 5.0 cm in front of a converging lens of focal length 20 cm. An observer sees an image of the object formed on the opposite side of the lens to where the object is located.

How far from the lens is the image?

What is the height of the image?

Q7:

A lens has a focal length of 20 cm. Parallel light rays from a distant source strike the lens at an angle of 1 5 from its optical axis. Find the distance from the axis of the real image observed on a screen in the focal plane of the lens.

Q8:

Find the focal length of a thin plano-convex lens. The front surface of this lens is flat, and the rear surface has a radius of curvature of 3 5 cm. The refractive index of the lens is 1.5.

Q9:

A diverging lens has a focal length of 20 cm. What is the power of the lens in diopters?

Q10:

An object of height 3.0 cm is placed at 25 cm in front of a diverging lens of focal length 20 cm. Behind the diverging lens, there is a converging lens of focal length 20 cm. The distance between the lenses is 5.0 cm.

How far to the right of the converging lens is the final image formed?

What is the height of the final image?

Q11:

A camera has a lens with a focal length of 35.0 mm and is being used to form an image of a flower 55.0 cm in front of the lens. How far behind the lens is the camera’s photosensor?

Q12:

A telephoto lens with a focal length of 300 mm is being used to photograph mountains located 12.0 km away.

How far behind the lens is the image of the mountain formed?

What is the height of the image of a 2 3 0 0 m high cliff on one of the mountains?

Q13:

An object of height 4.60 cm is placed at 6.00 cm in front of a lens of focal length 25.0 cm and observed from the opposite side of the lens.

What is the distance between the image formed and the center of the lens?

What is the height of the image formed?

Q14:

A camera lens used for taking close-up photographs has a focal length of 22.0 mm. The farthest the lens can be placed from the camera’s photosensor is 33.0 mm. At distances from the lens less than a distance 𝑑 m i n , it is not possible to produce an image that is in focus.

Find 𝑑 m i n .

What magnification is produced at 𝑑 m i n ?

Q15:

Find the focal length of a meniscus lens with radii of curvature 𝑅 1 = 29 cm and 𝑅 2 = 21 cm. Use a value of 1.5 for the refractive index of the lens material.

Q16:

Two convex lenses of focal lengths 25 cm and 13 cm, respectively, are placed 60 cm apart, with the lens of longer focal length on the right. An object of height 2.5 cm is placed equidistantly between the lenses and observed through each lens from the left and from the right.

What is the distance between the right-hand lens and the object image produced by it?

What is the distance between the left-hand lens and the object image produced by it?

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