Two thin lenses, one of focal length + 60 cm and the other of focal length – 20 cm are put in contact. The combined focal length is

Options

A. `=15 cm`
B. `-15cm`
C. `=30 cm`
D. `-30 cm`

Explanation

To find the combined focal length of two thin lenses in contact, we can follow these steps:

### Step 1: Identify the Focal Lengths
We have two lenses:
- Lens 1 (Convex lens): Focal length \( F_1 = +60 \, \text{cm} \)
- Lens 2 (Concave lens): Focal length \( F_2 = -20 \, \text{cm} \)

### Step 2: Use the Formula for Combined Focal Length
The formula for the combined focal length \( F \) of two lenses in contact is given by:
\[ \frac{1}{F} = \frac{1}{F_1} + \frac{1}{F_2} \]

### Step 3: Substitute the Values
Substituting the values of \( F_1 \) and \( F_2 \) into the formula:
\[ \frac{1}{F} = \frac{1}{60} + \frac{1}{-20} \]

### Step 4: Find a Common Denominator
To add the fractions, we need a common denominator. The least common multiple of 60 and 20 is 60. Thus:
\[ \frac{1}{F} = \frac{1}{60} - \frac{3}{60} = \frac{1 - 3}{60} = \frac{-2}{60} \]

### Step 5: Simplify the Expression
Now, simplify the expression:
\[ \frac{1}{F} = \frac{-2}{60} = \frac{-1}{30} \]

### Step 6: Calculate the Combined Focal Length
Taking the reciprocal gives us:
\[ F = -30 \, \text{cm} \]

### Final Answer
The combined focal length of the two lenses is \( F = -30 \, \text{cm} \).

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