Question

Keesha is looking at a beetle with a magnifying glass. She wants to see an upright, enlarged image at a distance of \(25 \mathrm{cm} .\) The focal length of the magnifying glass is \(+5.0 \mathrm{cm} .\) Assume that Keesha's eye is close to the magnifying glass. (a) What should be the distance between the magnifying glass and the beetle? (b) What is the angular magnification? (tutorial: magnifying glass II).

Short answer

Answer: The distance between the magnifying glass and the beetle is 6.25 cm, and the angular magnification of the magnifying glass is 5.

Step-by-step solution

Recall the lens formula

First, we need to recall the lens formula, which relates the object distance (p), the image distance (q), and the focal length (f) as follows: \( \frac{1}{f} = \frac{1}{p} + \frac{1}{q} \)

Plug in the values

We are given that the image distance (q) is \(25 \mathrm{cm}\) and the focal length (f) is \(+5.0 \mathrm{cm}\). Plugging these values into the lens formula, we get: \( \frac{1}{+5.0} = \frac{1}{p} + \frac{1}{25} \)

Solve for the object distance

To find the object distance (p), we can rearrange and solve the equation: \( \frac{1}{p} = \frac{1}{+5.0} - \frac{1}{25} \) \( \frac{1}{p} = \frac{4}{25} \) \( p = \frac{25}{4} \) \( p = 6.25 \mathrm{cm} \) So the distance between the magnifying glass and the beetle should be \(6.25 \mathrm{cm}\).

Recall the formula for angular magnification

Next, let's find the angular magnification. Recall the formula for angular magnification (M): \( M = \frac{25 \mathrm{cm}}{f} \)

Plug in the values and solve for angular magnification

Now, we can plug in the values for the image distance (q) and the focal length (f) to find the angular magnification: \( M = \frac{25}{5.0} \) \( M = 5 \) The angular magnification of the magnifying glass is 5. So, the distance between the magnifying glass and the beetle should be \(6.25 \mathrm{cm}\), and the angular magnification is 5.