Question

Focal length of each lens is 10 cm as shown in the given figure. Find the distance of the image of point object O from the convex lens and also draw the ray diagram. If both lenses are placed in contact, what will be the power of the combined lens? 

Hint:

When convex and concave lenses of equal focal length are combined, they cancel each other out.

Answer 1

Step 1: Using the lens formula for the convex lens: \[ \frac{1}{f} = \frac{1}{v} - \frac{1}{u} \] \[ \frac{1}{10} = \frac{1}{v} - \frac{1}{-20} \] \[ \frac{1}{v} = \frac{1}{10} + \frac{1}{20} = \frac{3}{20} \] \[ v = \frac{20}{3} \approx 6.67 \text{ cm} \] Step 2: The image acts as an object for the concave lens. Using the lens formula again: \[ \frac{1}{-10} = \frac{1}{v'} - \frac{1}{30 - 6.67} \] \[ \frac{1}{-10} = \frac{1}{v'} - \frac{1}{23.33} \] \[ v' = -17.5 \text{ cm} \] \[ \boxed{\text{Image distance } = 17.5 \text{ cm behind concave lens.}} \] Step 3: For combined lenses in contact, the effective power is: \[ P_{\text{total}} = P_1 + P_2 \] \[ = \frac{100}{10} + \frac{100}{-10} \] \[ = 10 - 10 = 0 \, \text{D} \] \[ \boxed{\text{Total power } = 0 \text{ D (acts like a plane glass).}} \]