A simple telescope, consisting of an objective of focal length 60 cm and a single eye lens of focal length 5 cm is focussed on a distant object in such a way that parallel rays comes out from the eye lens. If the object subtends an angle `2^(@)` at the objective, the angular width of the image

Options

A. `10^(@)`
B. `24^(@)`
C. `50^(@)`
D. `(1//6)^(@)`

Explanation

To solve the problem of finding the angular width of the image formed by a simple telescope, we can follow these steps:

### Step 1: Understand the given values
- Focal length of the objective lens (Fo) = 60 cm
- Focal length of the eye lens (Fe) = 5 cm
- Angular width of the object (α) = 2 degrees

### Step 2: Calculate the magnification of the telescope
The magnification (M) of a simple telescope is given by the formula:
\[ M = \frac{F_o}{F_e} \]
Substituting the given values:
\[ M = \frac{60 \text{ cm}}{5 \text{ cm}} = 12 \]

### Step 3: Relate the angular widths of the object and image
The relationship between the angular width of the object (α) and the angular width of the image (β) can be expressed using the magnification:
\[ M = \frac{\beta}{\alpha} \]
Rearranging this formula gives:
\[ \beta = M \times \alpha \]

### Step 4: Substitute the values to find the angular width of the image
Now, substituting the values we have:
\[ \beta = 12 \times 2 \text{ degrees} = 24 \text{ degrees} \]

### Step 5: Conclusion
Thus, the angular width of the image is 24 degrees.

### Final Answer:
The angular width of the image is 24 degrees.

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