If an objects is placed 10 cm from a convex mirror of radius of curvature 60 cm, then the position of image is

Options

A. 7 . 5cm
B. 6 . 5 cm
C. - 7 . 5 cm
D. 5 . 0 cm

Answer

To find the position of the image formed by a convex mirror when an object is placed 10 cm from it, we can use the mirror formula:

### Step-by-Step Solution:

1. **Identify Given Values:**
- Object distance (u) = -10 cm (the negative sign is used because the object is in front of the mirror)
- Radius of curvature (R) = 60 cm

2. **Calculate the Focal Length (f):**
- The focal length (f) of a convex mirror is given by the formula:
\[ f = \frac{R}{2} \]
- Substituting the value of R:
\[ f = \frac{60 \, \text{cm}}{2} = 30 \, \text{cm} \]
- Since it is a convex mirror, the focal length is positive:
\[ f = +30 \, \text{cm} \]

3. **Apply the Mirror Formula:**
- The mirror formula is given by:
\[ \frac{1}{v} + \frac{1}{u} = \frac{1}{f} \]
- Substituting the values of u and f:
\[ \frac{1}{v} + \frac{1}{-10} = \frac{1}{30} \]

4. **Rearranging the Equation:**
- Rearranging gives:
\[ \frac{1}{v} = \frac{1}{30} + \frac{1}{10} \]
- To add the fractions, find a common denominator (which is 30):
\[ \frac{1}{10} = \frac{3}{30} \]
- Therefore:
\[ \frac{1}{v} = \frac{1}{30} + \frac{3}{30} = \frac{4}{30} \]

5. **Calculate v:**
- Taking the reciprocal gives:
\[ v = \frac{30}{4} = 7.5 \, \text{cm} \]

6. **Conclusion:**
- The position of the image is 7.5 cm behind the mirror (since for a convex mirror, the image distance is positive).

### Final Answer:
The position of the image is 7.5 cm behind the convex mirror.

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