Question

4. A real image¹/5th the size of the object is formed at a distance of 18 cm, from a mirror
The local length of this mirror is
a) -20 cm
(b) -15 cm
o +20 cm
(d)
+15 a​

Answer 1

Answer:

Given -

• A real image is 1/5th the size of the object and formed at a distance of 18cm.

To Find -

• Focal length of the mirror

Solution -

• Image distance, v = -18 cm
• Magnification = -1/5 ( as the image is real & inverted ).

We know that,

$\\ \\ \sf \: m = - \dfrac {v}{u} \\ \\ \\ \implies \sf \: - \dfrac{1}{5} = - \bigg( - \dfrac{18}{u} \bigg) \\ \\ \\ \implies \sf \: u = -( 5 \times 18) \\ \\ \\ \implies \sf \blue { u = - 90 \: cm}$

Therefore, u = -90 cm.

• Now, for focal length we'll apply the lens formula,

$\\ \\ \sf \: \dfrac{1}{f} = \dfrac{1}{v} + \dfrac{1}{u} \\ \\ \\ \implies \sf \: \dfrac{1}{f} = \dfrac{1}{ - 18} + \dfrac{1}{ - 90} \\ \\ \\ \implies \sf \: \dfrac{1}{f} = \frac{ - 5 - 1}{90} \\ \\ \\ \implies \sf \green{ f = - 15cm}$

Therefore, correct option is (b) i.e -15 cm.