A thin lens with a focal length of 6.00 cm is used as a simple magnifier. (a) What angular magnification is obtainable with the lens if the object is at the focal point?

Verified step by step guidance

1. Identify the focal length of the lens, which is given as 6.00 cm.
2. Understand that when an object is placed at the focal point of a lens, the image formed is at infinity. This is because the rays of light coming from the object are parallel after passing through the lens.
3. Recall the formula for angular magnification (M) when using a lens as a magnifier: M = 1 + \( \frac{D}{f} \), where D is the least distance of distinct vision (typically about 25 cm for a normal human eye) and f is the focal length of the lens.
4. Since the object is at the focal point, the formula simplifies to M = \( \frac{D}{f} \) because the image is at infinity and the first term (1) becomes negligible.
5. Substitute the values of D and f into the formula to find the angular magnification.

Key Concepts

Focal Length

The focal length of a lens is the distance from the lens to the point where parallel rays of light converge or appear to diverge. For a thin lens, this distance is crucial in determining how the lens will magnify an object. In this case, a focal length of 6.00 cm indicates that the lens can focus light at this distance, which is essential for calculating magnification.

Angular Magnification

Angular magnification is a measure of how much larger an object appears when viewed through a lens compared to the naked eye. It is defined as the ratio of the angle subtended by the image at the eye to the angle subtended by the object at the same eye without the lens. For a simple magnifier, this is particularly relevant when the object is placed at the focal point, maximizing the apparent size of the image.

Simple Magnifier

A simple magnifier is a type of optical device, typically a convex lens, used to enlarge the appearance of an object. When an object is placed at or near the focal point of the lens, the lens produces a virtual image that appears larger than the object itself. Understanding how a simple magnifier works is essential for calculating the angular magnification in this scenario.