In a terrestrial telescope, the focal length of objective is `90cm` and of eye lens is `6 cm`. If the final image is at `30cm`, then the magnification will be

Options

A. 21
B. 12
C. 18
D. 15

Answer

To find the magnification of a terrestrial telescope, we can use the formula for magnifying power (M) of the telescope, which is given by:

\[ M = \frac{F_o}{F_e} \left(1 + \frac{D}{F_e}\right) \]

Where:
- \( F_o \) = Focal length of the objective lens
- \( F_e \) = Focal length of the eyepiece lens
- \( D \) = Least distance of distinct vision (typically taken as 25 cm for normal vision, but in this case, it is given as 30 cm)

Given:
- \( F_o = 90 \, \text{cm} \)
- \( F_e = 6 \, \text{cm} \)
- \( D = 30 \, \text{cm} \)

### Step 1: Substitute the values into the formula

Substituting the given values into the magnification formula:

\[ M = \frac{90}{6} \left(1 + \frac{30}{6}\right) \]

### Step 2: Simplify the first part of the equation

Calculating \( \frac{90}{6} \):

\[ \frac{90}{6} = 15 \]

### Step 3: Calculate the second part of the equation

Now calculate \( 1 + \frac{30}{6} \):

\[ \frac{30}{6} = 5 \]

So,

\[ 1 + 5 = 6 \]

### Step 4: Combine the results

Now substitute back into the equation:

\[ M = 15 \times 6 \]

### Step 5: Final calculation

Calculating the final value:

\[ M = 90 \]

Thus, the magnification of the terrestrial telescope is **90**.

### Summary of Steps:
1. Write down the magnification formula.
2. Substitute the given values.
3. Simplify the first part of the equation.
4. Calculate the second part of the equation.
5. Combine the results to find the final magnification.