Question

A converging lens will be used as a magnifying glass. In order for this to work, the object must be placed at a distance a) \(d_{\mathrm{o}}>f\). c) \(d_{\mathrm{o}}

Short answer

a) \(d_o > f\) b) \(d_o = f\) c) \(d_o < f\) Answer: c) \(d_o < f\)

Step-by-step solution

Conditions for magnification

A lens works as a magnifying glass when it produces a virtual, upright, and magnified image of the object. For a converging lens to produce such an image, the object must be placed within its focal length, meaning that it should be closer to the lens than the focal length. In other words, the object distance \(d_o < f\). Now let's check each of the given options to see which one matches the condition we found.

Evaluate option a

Option a suggests that the object should be placed at a distance \(d_o > f\). If the object is placed at a position farther than the focal length, the converging lens will produce a real and inverted image instead of a virtual and upright one. Hence, the lens will not work as a magnifying glass in this case. So, option a is an incorrect choice.

Evaluate option b

Option b suggests that the object should be placed at a distance \(d_o = f\), which means the object will be placed exactly at the focal point on the object side. In this case, the converging lens will form an image at infinity, which is not useful for magnification either. Therefore, option b is also an incorrect choice.

Evaluate option c

Option c suggests that the object should be placed at a distance \(d_o < f\). As we mentioned in Step 1, placing the object at a distance less than the lens' focal length produces a virtual, upright, and magnified image, which is the desired condition for a magnifying glass. Thus, option c is the correct choice. Hence, the right distance to place the object for a converging lens to work as a magnifying glass is \(d_o < f\), making option (c) the correct answer.

Key concepts

Converging Lens

A converging lens, also known as a convex lens, is thicker in the middle than at the edges. This shape allows it to focus light rays to a point known as the focal point. When parallel light rays strike a converging lens, they are bent inwards and come together at this focal point.

Converging lenses are crucial in various optical devices like cameras, eyeglasses, and microscopes. Their ability to focus light enables them to enlarge images, making them very useful in magnifying glasses.

When you place an object within the focal length of a converging lens, it creates certain types of images. For the lens to serve as a magnifying glass, the object must be placed closer than the focal length, a key factor in magnification.

Magnification

Magnification refers to the process of enlarging the appearance of an object through optical instruments like lenses. In a converging lens, magnification occurs when the lens creates a virtual image that appears larger than the actual object.

Here are a few important points about magnification using a converging lens:

• An object must be within the focal length of the lens for magnification to occur.
• In this scenario, the lens produces a virtual image that appears on the same side as the object.
• This image is upright and magnifies the appearance of the object.

This process of producing a virtual and magnified image is what makes lenses work as magnifying glasses. Magnification helps in viewing tiny details that are difficult to see with the naked eye.

Focal Length

The focal length of a lens is a critical measurement that determines how strongly the lens converges or diverges light. It is defined as the distance between the center of the lens and its focal point.

Key characteristics of focal length in a converging lens include:

• A shorter focal length means a stronger lens that bends light more severely.
• Focal length affects the magnification power of the lens.
• For a converging lens acting as a magnifying glass, the object should be placed within the focal length to create a magnified image.

Understanding focal length is important in using lenses effectively. If the object is farther than the focal length, the lens will not work as a magnifying glass because it won't generate a virtual and enlarged image. Therefore, knowing and appropriately using the focal length is crucial for tasks involving optical magnification.