Distance between object and its image (magnified by -1/3) is 30 cm. The focal length of the mirror used is (x/4)cm, where magnitude of value of x is _________. Numerical answer type. Work it out, then open the answer.

Answer: 45. m = -v/u = -1/3 ⇒ v = u/3 (real image, concave mirror). Object-image distance = |u| - |u|/3 = 2|u|/3 = 30 ⇒ u = -45 cm, v = -15 cm 1/f = -1/15 - 1/45 = -4/45 ⇒ f = -45/4 cm |x| = 45

Distance between object and its image (magnified by -1/3) is 30 cm… | JEE Main 2025 (4 Apr, Shift 1)

Q8JEE Main 2025 · 4 APR · SHIFT 1Medium

Reflection & Mirrors

Distance between object and its image (magnified by $-\frac{1}{3}$ ) is 30 cm. The focal length of the mirror used is $\left(\frac{x}{4}\right)\text{cm}$ , where magnitude of value of $x$ is _________.

Numerical answer type. Work it out, then open the answer.

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Answer: 45

$m = -\frac{v}{u} = -\frac{1}{3} \Rightarrow v = \frac{u}{3}$ (real image, concave mirror).
Object-image distance $= |u| - \frac{|u|}{3} = \frac{2|u|}{3} = 30 \Rightarrow u = -45\text{ cm}$ , $v = -15\text{ cm}$
$\frac{1}{f} = -\frac{1}{15} - \frac{1}{45} = -\frac{4}{45} \Rightarrow f = -\frac{45}{4}\text{ cm}$
$|x| = 45$

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