Question

""An object is placed in front of a convex mirror with a radius of curvature of 20 cm. Its image is formed 8 cm behind the mirror. Find the distance of the object from the mirror.

Please calculate and provide the distance of the object from the mirror.""

Answer 1

The distance of the object from the convex mirror is _12.8 cm_. This is determined by applying the mirror formula, which is 1/f = 1/v + 1/u, where f is the focal length, v is the image distance, and u is the object distance.

Step-by-step explanation:

In the given scenario, we are dealing with a convex mirror with a radius of curvature (R) of 20 cm. The focal length (f) of the convex mirror is half of the radius of curvature, so f = R/2 = 20/2 = 10 cm. The image distance (v) is given as 8 cm behind the mirror. Now, using the mirror formula, 1/f = 1/v + 1/u, we can solve for the object distance (u).

Starting with the mirror formula:

`\[ (1)/(f) = (1)/(v) + (1)/(u) \]`

Substitute the given values:

`\[ (1)/(10) = (1)/(8) + (1)/(u) \]`

To find u, we can rearrange the equation:

`\[ (1)/(u) = (1)/(10) - (1)/(8) \]`

Combine the fractions:

`\[ (1)/(u) = (4)/(40) - (5)/(40) \]`

Simplify further:

`\[ (1)/(u) = -(1)/(40) \]`

Finally, solve for u:

`\[ u = -40 \, \text{cm} \]`

The negative sign indicates that the object is on the same side as the incident light. Therefore, the object distance (u) is 40 cm. However, since we are interested in the magnitude of the distance, the final answer is 40 cm.