Question

Two lenses, one diverging of power 2D and the other converging of power 6D are combined together. Calculate the focal length and power of combination.

Hint:

The power of a combination of lenses is the sum of the individual powers. A negative total power indicates a diverging lens.

Answer 1

Step 1: Formula for power of combination.
The total power \( P_{\text{comb}} \) of two lenses in contact is the sum of the individual powers: \[ P_{\text{comb}} = P_1 + P_2 \] where \( P_1 = 2 \, \text{D} \) (diverging) and \( P_2 = 6 \, \text{D} \) (converging). Step 2: Calculating the total power.
\[ P_{\text{comb}} = 2 + (-6) = -4 \, \text{D} \] The negative sign indicates that the combination is a diverging lens. Step 3: Calculating the focal length.
The focal length \( f_{\text{comb}} \) is related to the power by: \[ f_{\text{comb}} = \frac{1}{P_{\text{comb}}} \] Substituting the value of \( P_{\text{comb}} \): \[ f_{\text{comb}} = \frac{1}{-4} = -0.25 \, \text{m} \] Step 4: Conclusion.
Thus, the focal length of the combination is \( -0.25 \, \text{m} \), and the power of the combination is \( -4 \, \text{D} \).