An object is placed at a distanced of 15 cm from a thin concave(diverging) lens along its axis. The lens has a focal length of magnitude 10 cm. What are values of image distance and magnification

To find the image distance (\(v\)) and magnification (\(m\)) for a thin concave (diverging) lens, we can use the lens formula and the magnification formula.

1. **Lens formula**:
   \[
   \frac{1}{f} = \frac{1}{v} + \frac{1}{u}
   \]
   where:
   - \(f = -10\) cm (focal length for a concave lens is negative),
   - \(u = -15\) cm (object distance is negative for real objects).

Plugging in the values:
\[
\frac{1}{-10} = \frac{1}{v} + \frac{1}{-15}
\]
This simplifies to:
\[
\frac{1}{v} = -\frac{1}{10} + \frac{1}{15}
\]
Finding a common denominator (30):
\[
\frac{1}{v} = -\frac{3}{30} + \frac{2}{30} = -\frac{1}{30}
\]
Thus,
\[
v = -30 \text{ cm}
\]

2. **Magnification formula**:
   \[
   m = -\frac{v}{u}
   \]
Substituting the values:
\[
m = -\frac{-30}{-15} = 2
\]

**Summary**:
- Image distance \(v = -30\) cm (indicating a virtual image on the same side as the object).
- Magnification \(m = 2\) (the image is upright and twice the size of the object).

Do you want details or have any questions? Here are some related questions:
1. What is the significance of the sign convention in optics?
2. How does the magnification relate to the type of lens used?
3. Can you explain how to draw a ray diagram for this scenario?
4. What happens to the image characteristics if the object distance changes?
5. How does the focal length affect the image distance and magnification? 

**Tip**: Always remember to apply the correct sign conventions for lens formulas to avoid confusion in calculations.

An object is placed at a distance of 15 cm from a thin concave (diverging) lens along its axis. The lens has a focal length of magnitude 10 cm. What are values of image distance and magnification?

Discover how to calculate the image distance and magnification for an object 15 cm away from a concave lens with a 10 cm focal length. Using the lens formula and magnification formula, this example provides a step-by-step solution, ideal for students in Grades 10-12 studying optics.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation