1. Given data

• Distance between object and image $= 20\,\text{cm}$
• Magnification $m = -3$
• For a mirror, magnification is $m = -\frac{v}{u}$

So, $-\frac{v}{u} = -3 \implies \frac{v}{u} = 3 \implies v = 3u$

2. Use the object-image separation

For a concave mirror forming a real image, object and image are on the same side of the mirror. Since $|v| > |u|$ here, the separation is $|v-u| = 20$

Using $v = 3u$, $|3u-u| = 20$ $|2u| = 20$ $|u| = 10\,\text{cm}$

Thus, $|v| = 30\,\text{cm}$

Using Cartesian sign convention for a concave mirror: $u = -10\,\text{cm}, \quad v = -30\,\text{cm}$

3. Apply mirror formula

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

Substitute values: $\frac{1}{f} = \frac{1}{-30} + \frac{1}{-10}$ $\frac{1}{f} = -\frac{1}{30} - \frac{1}{10} = -\frac{1}{30} - \frac{3}{30} = -\frac{4}{30} = -\frac{2}{15}$

So, $f = -\frac{15}{2} = -7.5\,\text{cm}$

4. Find radius of curvature

$R = 2f$ $R = 2(-7.5) = -15\,\text{cm}$

Hence the magnitude of radius of curvature is $|R| = 15\,\text{cm}$

5. Option check

• A: $3.75\,\text{cm}$ — incorrect
• B: $15\,\text{cm}$ — correct
• C: $7.5\,\text{cm}$ — incorrect
• D: $30\,\text{cm}$ — incorrect

Therefore, the correct answer is B.