A convex lens of focal length 15 cm is placed on a plane mirror. An object is placed at 30 cm from the lens. The image is

Options

A. real, at 30 cm in front of the mirror
B. real, at 30 cm behind the mirror
C. real, at 10 cm in front of the mirror
D. virtual, at 10 cm behind the mirror

Explanation

To solve the problem, we will follow these steps:

### Step 1: Understand the setup
We have a convex lens with a focal length (f) of 15 cm placed on a plane mirror. An object is placed at a distance (u) of 30 cm from the lens.

### Step 2: Determine the image formation by the lens
Using the lens formula:
\[ \frac{1}{f} = \frac{1}{u} + \frac{1}{v} \]
where:
- \( f \) = focal length of the lens = 15 cm
- \( u \) = object distance = -30 cm (the object distance is taken as negative in lens formula)

### Step 3: Substitute the values into the lens formula
Substituting the values into the lens formula:
\[ \frac{1}{15} = \frac{1}{-30} + \frac{1}{v} \]

### Step 4: Solve for \( \frac{1}{v} \)
Rearranging the equation gives:
\[ \frac{1}{v} = \frac{1}{15} + \frac{1}{30} \]

### Step 5: Find a common denominator
The common denominator for 15 and 30 is 30. Therefore:
\[ \frac{1}{15} = \frac{2}{30} \]
So,
\[ \frac{1}{v} = \frac{2}{30} + \frac{1}{30} = \frac{3}{30} \]

### Step 6: Calculate \( v \)
Thus,
\[ \frac{1}{v} = \frac{1}{10} \implies v = 10 \text{ cm} \]

### Step 7: Determine the position of the image
Since the image formed by the lens is at 10 cm, and the lens is placed on a plane mirror, the image will be real and will be formed in front of the mirror.

### Final Answer
The image is real and located at 10 cm in front of the mirror.

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