Given data

• Concave mirror focal length: $f = 0.4\,\text{m}$
• Required image: upright with magnification $m = 5$

Sign convention For a concave mirror, using Cartesian sign convention:

• $f = -0.4\,\text{m}$
• Object distance $u < 0$
• For an upright image in a concave mirror, the image is virtual, so $v > 0$

Use magnification formula For mirrors, $m = -\frac{v}{u}$ Given $m=5$, $5 = -\frac{v}{u}$ $v = -5u$

Use mirror formula $\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$ Substitute $f=-0.4$ and $v=-5u$: $\frac{1}{-0.4} = \frac{1}{-5u} + \frac{1}{u}$ $-2.5 = -\frac{1}{5u} + \frac{1}{u}$ Take LCM: $-2.5 = \frac{-1+5}{5u} = \frac{4}{5u}$ $-2.5 = \frac{4}{5u}$ $-12.5u = 4$ $u = -0.32\,\text{m}$

Interpretation The negative sign shows the object is in front of the mirror, as expected. Hence the required distance from face to mirror is $|u| = 0.32\,\text{m}$

Check options

• A: $0.24\,\text{m}$
• B: $0.32\,\text{m}$
• C: $1.60\,\text{m}$
• D: $0.16\,\text{m}$

Therefore, the correct option is B.