A 5 cm tall object is placed 50 cm from a concave mirror. The radius of curvature of the mirror is 60 cm. The image will form at ________________cm away from the mirror

To determine the location of the image formed by a concave mirror, we can use the mirror equation:

\[
\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}
\]

where:
- \( f \) is the focal length of the mirror,
- \( d_o \) is the object distance,
- \( d_i \) is the image distance.

First, we need to find the focal length \( f \). The focal length is related to the radius of curvature \( R \) by:

\[
f = \frac{R}{2}
\]

Given that the radius of curvature \( R \) is 60 cm, we have:

\[
f = \frac{60 \, \text{cm}}{2} = 30 \, \text{cm}
\]

Next, we substitute \( f = 30 \, \text{cm} \) and \( d_o = 50 \, \text{cm} \) into the mirror equation to find \( d_i \):

\[
\frac{1}{30} = \frac{1}{50} + \frac{1}{d_i}
\]

Rearranging to solve for \( \frac{1}{d_i} \):

\[
\frac{1}{d_i} = \frac{1}{30} - \frac{1}{50}
\]

Finding a common denominator (1500) to subtract the fractions:

\[
\frac{1}{30} = \frac{50}{1500}, \quad \frac{1}{50} = \frac{30}{1500}
\]

\[
\frac{1}{d_i} = \frac{50}{1500} - \frac{30}{1500} = \frac{20}{1500} = \frac{2}{150} = \frac{1}{75}
\]

Therefore,

\[
d_i = 75 \, \text{cm}
\]

So, the image will form 75 cm away from the mirror.

Do you want details or have any questions?

Here are 8 related questions to expand your understanding:

1. What is the relationship between the focal length and the radius of curvature for a concave mirror?
2. How does the object distance affect the image distance in concave mirrors?
3. What happens to the image if the object is placed at the focal point of a concave mirror?
4. Can a concave mirror form a virtual image? Under what conditions?
5. How would the image distance change if the object were moved closer to the mirror?
6. What is the magnification formula for mirrors, and how does it relate to object and image distances?
7. How does the size of the image compare to the size of the object in a concave mirror?
8. How would the image formation change if the mirror were convex instead of concave?

**Tip:** When using the mirror equation, always ensure the correct sign convention for distances: object distances are positive for real objects, and image distances are positive for real images and negative for virtual images.

Learn how to calculate the image distance formed by a concave mirror when an object 5 cm tall is placed 50 cm away from it. Detailed step-by-step solution using the mirror equation with a concave mirror radius of curvature 60 cm. Suitable for high school students studying optics.

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