A ray reflected successively from two plane mirrors incline at a certain angle undergoes a deviation of `240^@`. Then the number of images observable is

Options

A. 3
B. 5
C. 7
D. 9

Explanation

To solve the problem of finding the number of images observable when a ray is reflected successively from two plane mirrors inclined at a certain angle, we can follow these steps:

### Step 1: Understand the angle of deviation
The total angle of deviation (D) given in the problem is 240 degrees. The relationship between the angle of deviation and the angle (θ) between the two mirrors is given by the formula:
\[ D = 360 - 2\theta \]

### Step 2: Set up the equation
From the formula, we can rearrange it to find θ:
\[ 2\theta = 360 - D \]
Substituting the value of D:
\[ 2\theta = 360 - 240 \]

### Step 3: Calculate θ
Now, calculate the value of θ:
\[ 2\theta = 120 \]
\[ \theta = \frac{120}{2} = 60 \text{ degrees} \]

### Step 4: Use the formula for the number of images
The formula for the number of images (n) formed by two mirrors inclined at an angle θ is:
\[ n = \frac{360}{\theta} \]
Substituting the value of θ:
\[ n = \frac{360}{60} \]

### Step 5: Calculate n
Now, calculate n:
\[ n = 6 \]

### Step 6: Adjust for coinciding images
Since the number of images (n) is even, we need to subtract 1 from it to account for the coinciding images:
\[ \text{Total number of images} = n - 1 = 6 - 1 = 5 \]

### Conclusion
Thus, the total number of observable images is 5.

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