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Chapter 10: Problem 4

A spherical mirror and a thin spherical lens have each a focal length of \(-15 \mathrm{~cm}\). The mirror and the lens are likely to be (a) both concave. (b) both convex. (c) the mirror is concave and the lens is convex. (d) the mirror is convex, but the lens is concave.

Short Answer

Expert verified
Both the mirror and the lens are concave.

Step by step solution

01

Understand the given focal length

Both the spherical mirror and the thin spherical lens have a focal length of \( -15 \,\mathrm{cm} \). The negative sign indicates that the focal points are on the same side as the incoming light for mirrors and lenses.
02

Determine the types of mirror and lens with negative focal length

For a spherical mirror, a negative focal length means the mirror is concave. For a thin spherical lens, a negative focal length indicates a concave lens since it diverges light rays.
03

Match the correct option

From the information above, the correct option is that the mirror is concave, and the lens is concave. Therefore, the correct option is not listed exactly as described, but understanding that both are concave helps to conclude they must be concave.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

concave mirrors
Concave mirrors are a type of spherical mirror where the reflecting surface curves inward, like the inside of a bowl. This shape causes light rays that strike the mirror to converge, or come together, at a focal point. The focal point of a concave mirror is where the reflected light rays meet.
To understand the behavior of concave mirrors, remember these key points:
  • The focal length is the distance between the mirror's surface and the focal point.
  • A concave mirror's focal length is always negative. This is because the focal point is on the same side as the incoming light.

Concave mirrors are commonly used in devices like telescopes, flashlights, and makeup mirrors. They create real, inverted images when the object is placed outside the focal length. Conversely, if the object is within the focal length, the mirror will produce a virtual, upright, and magnified image.
concave lenses
Concave lenses are thin lenses that curve inward, resembling the shape of a cave. These lenses diverge light rays, which means they spread the light outwards. This behavior is opposite to that of concave mirrors.
Key features of concave lenses include:
  • They have a negative focal length.
  • The focal length is negative because the focal point is on the same side as the incoming light.

Because concave lenses diverge light rays, they are used to correct vision problems like myopia (nearsightedness). In this case, the lens helps to diverge light before it reaches the eye, allowing a person to see distant objects more clearly.
Another common application is in laser beams where they help to spread the light. When using a concave lens, the image formed is always virtual, upright, and smaller than the object.
negative focal length
The concept of negative focal length is essential in understanding optical devices like mirrors and lenses. A negative focal length means the focal point, where the light rays converge or appear to diverge from, is on the same side as the incoming light.
In the context of the exercise:
  • For concave mirrors, a negative focal length signifies that the focal point is in front of the mirror.
  • In concave lenses, the negative focal length indicates that the diverging rays appear to come from a focal point in front of the lens.

The negative focal length plays a pivotal role in how these devices manipulate light.
By understanding this concept, you can better appreciate how various optical instruments function. Whether it's focusing light to a point or diverging it outwards, the negative focal length is a key descriptor in the behavior of concave mirrors and lenses.

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Most popular questions from this chapter

An object \(5.0 \mathrm{~cm}\) in length is placed at a distance of \(20 \mathrm{~cm}\) in front of a convex mirror of radius of curvature \(30 \mathrm{~cm}\). Find the position of the image, its nature and size.

The magnification produced by a plane mirror is \(+1 .\) What does this mean?

An object of size \(7.0 \mathrm{~cm}\) is placed at \(27 \mathrm{~cm}\) in front of a concave mirror of focal length \(18 \mathrm{~cm}\). At what distance from the mirror should a screen be placed, so that a sharp focussed image can be obtained? Find the size and the nature of the image.

Name the type of mirror used in the following situations. (a) Headlights of a car. (b) Side/rear-view mirror of a vehicle. (c) Solar furnace. Support your answer with reason.

A doctor has prescribed a corrective lens of power \(+1.5 \mathrm{D}\). Find the focal length of the lens. Is the prescribed lens diverging or converging?
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