In the following diagram focal length of convex lens is 20 cm. What is the focal length of concave lens?

30 cm

The correct answer is Option (1) → 30 cm

Light rays are parallel before entering the convex lens, so:

Convex lens forms image at its focal point

$f_1 = 20 \text{ cm}$

So, rays converge to a point 20 cm to the right of convex lens

Step 1: Distance between lenses

From diagram: distance between lenses $= 5 \text{ cm}$

So, for concave lens:

Object distance $=$ distance of this image from concave lens

$u = 20 - 5 = 15 \text{ cm}$

Since object is on right side of concave lens:

$u = +15 \text{ cm}$

Step 2: Final image position

Final image is 30 cm to the right of concave lens

$v = +30 \text{ cm}$

Step 3: Lens formula

$\frac{1}{f} = \frac{1}{v} - \frac{1}{u}$

$\frac{1}{f} = \frac{1}{30} - \frac{1}{15}$

$\frac{1}{f} = \frac{1 - 2}{30} = \frac{-1}{30}$

$f = -30 \text{ cm}$

Step 4: Interpretation

Negative sign $\rightarrow$ concave lens

Magnitude $= 30 \text{ cm}$