Two thin concave lenses of focal lengths 10 cm and 30 cm and a thin convex lens of focal length 30 cm are kept in contact. What will be the power of lens combination ?

Options

A. `+10 D `
B. `-10 D`
C. `-3.33 D`
D. `+3.33`

Explanation

To find the power of the lens combination consisting of two thin concave lenses and one thin convex lens, we can follow these steps:

### Step 1: Identify the focal lengths of the lenses
- The focal length of the first concave lens (f1) = -10 cm (since it is concave, it is negative).
- The focal length of the second concave lens (f2) = -30 cm (also negative).
- The focal length of the convex lens (f3) = +30 cm (since it is convex, it is positive).

### Step 2: Convert focal lengths to meters
- f1 = -10 cm = -0.1 m
- f2 = -30 cm = -0.3 m
- f3 = +30 cm = +0.3 m

### Step 3: Calculate the power of each lens
The power (P) of a lens is given by the formula:
\[ P = \frac{1}{f} \]
where \( f \) is the focal length in meters.

- Power of the first lens (P1):
\[ P_1 = \frac{1}{f_1} = \frac{1}{-0.1} = -10 \, \text{D} \]

- Power of the second lens (P2):
\[ P_2 = \frac{1}{f_2} = \frac{1}{-0.3} = -\frac{10}{3} \, \text{D} \approx -3.33 \, \text{D} \]

- Power of the third lens (P3):
\[ P_3 = \frac{1}{f_3} = \frac{1}{0.3} = \frac{10}{3} \, \text{D} \approx 3.33 \, \text{D} \]

### Step 4: Calculate the total power of the lens combination
The total power of the lens combination (P) is the sum of the powers of the individual lenses:
\[ P = P_1 + P_2 + P_3 \]
Substituting the values:
\[ P = -10 + \left(-\frac{10}{3}\right) + \left(\frac{10}{3}\right) \]

Notice that \( -\frac{10}{3} + \frac{10}{3} = 0 \), so:
\[ P = -10 \, \text{D} \]

### Final Answer
The power of the lens combination is \( -10 \, \text{D} \).

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