A convex lens of power `2 D` and a concave lens of focal length
`40cm`are kept in contact, find
(a) Power of combination , (b) Equivalent focal length

Explanation

To solve the problem step by step, we will first find the power of the combination of the lenses and then calculate the equivalent focal length.

### Step 1: Identify the given values
- Power of the convex lens (P_convex) = 2 D
- Focal length of the concave lens (f_concave) = -40 cm (negative because it is a concave lens)

### Step 2: Convert the focal length of the concave lens to power
The power of a lens is given by the formula:
\[ P = \frac{1}{f} \]
where \( f \) is the focal length in meters.

For the concave lens:
\[ P_{concave} = \frac{1}{f_{concave}} = \frac{1}{-0.4 \text{ m}} = -2.5 \text{ D} \]

### Step 3: Calculate the total power of the combination
The total power of the combination of lenses in contact is given by:
\[ P_{total} = P_{convex} + P_{concave} \]

Substituting the values:
\[ P_{total} = 2 \text{ D} + (-2.5 \text{ D}) \]
\[ P_{total} = 2 \text{ D} - 2.5 \text{ D} \]
\[ P_{total} = -0.5 \text{ D} \]

### Step 4: Calculate the equivalent focal length
The equivalent focal length \( F \) can be calculated using the formula:
\[ F = \frac{1}{P} \]

Substituting the total power:
\[ F = \frac{1}{-0.5 \text{ D}} \]
\[ F = -2 \text{ m} \]

### Step 5: Convert the focal length to centimeters
Since 1 m = 100 cm,
\[ F = -2 \text{ m} = -200 \text{ cm} \]

### Final Answers
(a) Power of combination = -0.5 D
(b) Equivalent focal length = -200 cm

---