Worksheet: Images Produced by Thin Lenses

In this worksheet, we will practice relating the sizes and positions of objects to images of them produced by thin convex and concave lenses.

Q1:

An object is placed at the focal point of a thin concave lens. Which of the following statements most correctly describes how the distances from the object to the lens and from the image to the lens compare to each other?

  • AThe object distance from the lens is finite and the image distance from the lens is infinite.
  • BThe object distance from the lens is half the image distance from the lens.
  • CThe object distance from the lens is equal to the image distance from the lens.
  • DThe object distance from the lens is double the image distance from the lens.

Q2:

A thin convex lens is placed at a distance 𝑑  from an object 2.5 cm in height. On the opposite side of the lens, an image of the object is formed 16 cm from the lens. The distance from the object to the image is 36 cm.

Find 𝑑  .

What is the height of the image?

Q3:

An object is placed 2.5 cm from a thin convex lens with a focal length of 3.75 cm. The object is then moved away from the lens.

What is the initial distance between the object and the image?

What is the initial magnification produced by the lens?

How far would the object have to be moved for the lens to produce the same magnification that it produced initially, but with the image now real and inverted?

What is the distance between the initial image formed and the inverted image formed?

Q4:

A thin lens has a power of 4.5 diopters. What is the focal length of the lens?

Q5:

A thin lens, lens 𝐴 , has twice the optical power of another thin lens, lens 𝐡 . Lens 𝐴 has a focal length of 21 cm. What is the focal length of lens 𝐡 ?

Q6:

An image of an object 1.5 cm in height is formed by a thin lens. The magnification produced by the lens is – 2 . 2 .

Is the lens convex or concave?

  • AConvex
  • BConcave

What is the height of the image?

Q7:

A thin convex lens with a focal length of 2.1 cm is placed 4.5 cm away from an object. On the opposite side of the lens, an image of the object is formed. What is the distance from the lens to the image?

Q8:

Which of the following formulas correctly relates the magnification π‘š produced by a thin lens to the height β„Ž  of an object and the height β„Ž  of the image of the object produced by the lens?

  • A π‘š = β„Ž βˆ’ β„Ž  
  • B π‘š = β„Ž β„Ž  
  • C π‘š = β„Ž β„Ž  
  • D π‘š = β„Ž βˆ’ β„Ž  
  • E π‘š = β„Ž β„Ž  

Q9:

A thin convex lens is placed 15 cm away from an object. On the opposite side of the lens, an image of the object is formed that is 4.2 cm in height due to a magnification by the lens of – 3 . 6 .

What is the distance from the lens to the image?

What is the height of the object?

Q10:

Which of the following statements most correctly describes how the light rays from an object would have to be aligned with each other for a thin convex lens to form an image of the object at a point that is a distance from the lens equal to the focal length of the lens?

  • AThe light rays from the object would have to be emitted in all directions.
  • BThe light rays from the object would have to be parallel to each other.
  • CThe light rays from the object would have to be converging on a point.
  • DThe light rays from the object would have to be diverging from a point.

Q11:

A thin convex lens has a focal length of 4.8 cm. The lens is used to form an image of an object and produces a magnification of – 3 . 3 .

What is the distance from the lens to the image made by the lens?

What is the distance between the lens and the object that makes the image?

Q12:

A thin concave lens produces an image of an object. The image formed by the lens is 2.20 cm from the lens and the magnification produced by the lens is 0.75. Find the distance between the object that produces the image and the image.

Q13:

Which of the following formulas correctly relates the focal length, 𝑓 , of a thin lens to the optical power, 𝑃 , of the lens and the magnification, π‘š , produced by the lens?

  • A 𝑃 = 𝑓 π‘š
  • B 𝑃 = π‘š 𝑓
  • C 𝑃 = 1 π‘š
  • D 𝑃 = 1 𝑓 π‘š
  • E 𝑃 = 1 𝑓

Q14:

An object is placed at a distance from a thin convex lens equal to the focal length of the lens. Which of the following statements most correctly describes the formation of the image of the object?

  • AThe image will be formed on the same side of the lens as the object, and the distance between the object and the image will be the focal length of the lens.
  • BThe image will be formed on the same side of the lens as the object, and the distance between the object and the image will be the magnification produced by the lens.
  • CNo image will be formed as the light rays from each point on the object will be parallel to each other as they exit the lens and not converge on a focal point.
  • DThe image will be formed at the same distance from the lens as the object, but on the opposite side of the lens.
  • EThe light rays from the object will be totally internally reflected in the lens and no image will be formed.

Q15:

The thin lens shown in the diagram has a power of 12 diopters. Light is emitted from a point source at 𝑃 . One ray from 𝑃 is shown. At what distance from the center of the lens does the ray cross the lens’s optical axis on the side of its image?

Q16:

A thin concave lens has a focal length of 5.5 cm. An object is located 3.6 cm from the lens.

What is the distance from the lens to the image formed?

What is the magnification produced by the lens?

Q17:

Which of the following formulas correctly relates the focal length, 𝑓 , of a thin lens to the distance, 𝑑  , of an object from the lens and the distance, 𝑑  ,from the lens to the image of the object produced by the lens? A positive value of 𝑑  indicates distance on the opposite side of the lens to the object, and a negative value of 𝑑  indicates distance on the same side of the lens as the object. A positive value of 𝑓 corresponds to a distance on the opposite side of the lens to the object, and a negative value of 𝑓 corresponds to a distance on the same side of the lens as the object.

  • A 𝑓 = 𝑑 βˆ’ 𝑑  
  • B 1 𝑓 = 1 𝑑 βˆ’ 1 𝑑  
  • C 1 𝑓 = 1 𝑑 + 1 𝑑  
  • D 𝑓 = 𝑑 + 𝑑  
  • E 1 𝑓 = 1 𝑑 βˆ’ 1 𝑑  

Q18:

A thin lens produces an image of an object, 46 cm from the lens, on the opposite side of the lens to the object. The power of the lens is 2.4 diopters. What magnification is produced by the lens?

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