A Galilean telescope is 27 cm long when focussed to form an image at infinity. If the objective has a focal length of 30 cm, what is the focal length of the eyepiece?

Answer

To solve the problem, we will follow these steps:

### Step 1: Understand the components of a Galilean telescope
A Galilean telescope consists of two lenses: a convex lens (the objective) and a concave lens (the eyepiece). The objective lens is responsible for gathering light and forming an image, while the eyepiece lens magnifies this image for viewing.

### Step 2: Identify the given values
- Length of the telescope (L) = 27 cm
- Focal length of the objective lens (FO) = 30 cm
- Focal length of the eyepiece lens (FE) = ?

### Step 3: Use the formula relating the lengths
In a Galilean telescope, the relationship between the focal lengths and the length of the telescope can be expressed as:
\[ FO = L + FE \]

### Step 4: Substitute the known values into the equation
We can substitute the known values into the equation:
\[ 30 \, \text{cm} = 27 \, \text{cm} + FE \]

### Step 5: Solve for the focal length of the eyepiece
Now, we can rearrange the equation to find the focal length of the eyepiece:
\[ FE = 30 \, \text{cm} - 27 \, \text{cm} \]
\[ FE = 3 \, \text{cm} \]

### Final Answer
The focal length of the eyepiece (FE) is **3 cm**.

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