The focal length of a concave mirror is 2.0cm. If an object is placed 8.0cm from it, the image is at

Analysis

To solve this problem, we need to use the Mirror Formula, which relates the focal length ($f$), the object distance ($u$), and the image distance ($v$).

Concept

The mirror formula is given by:

Where:

• $f$ = focal length
• $u$ = object distance
• $v$ = image distance

Note on Sign Convention: For a concave mirror, the focal length ($f$) is positive.

Step-by-Step Solution

1. Identify the given values:

• Focal length ($f$) = 2.0 cm
• Object distance ($u$) = 8.0 cm

2. Rearrange the formula to solve for $v$:

3. Substitute the values into the equation:

4. Find a common denominator (which is 8.0):

5. Solve for $v$:

Rounding to one decimal place, we get 2.7 cm.

*Correction regarding the provided options:* The options provided in your question list the units as meters (m), but the calculation yields 2.7 cm. Given the context of JAMB questions, there is often a typographical error in the units of the options (using 'm' instead of 'cm'). Based on the numerical value, 2.7 matches option A.

Exam Tip

When dealing with mirror and lens problems, always remember the "Real is Positive" rule for mirrors:

• Concave mirror: $f$ is positive.
• Convex mirror: $f$ is negative.
• If your final answer for $v$ is positive, the image is real and formed in front of the mirror. If $v$ is negative, the image is virtual and formed behind the mirror.