Question

an object is placed 30 cm(from the reflecting surface) in front of a block of glass 10 cm thick having its farther side silvered. the final image is formed at 23.2 cm behind the silvered face. The refractive index of glass is :

• A. $1.41$
• B. $1.46$
• C. $200/132$
• D. $1.61$

Answer 1

The correct option is A $1.41$

D. to slah mirros will be shifted towards object

$\begin{array}{cc}\Rightarrow M{M}^{\prime }& =\left(10(1-\frac{1}{\mu })\right)\\ M{M}^{\prime }& =10-\frac{10}{\mu }\\ O{M}^{\prime }& =OM-M{M}^{\prime }\\ & =30+10-(10-\frac{10}{4})\\ & =30+\frac{10}{4}\end{array}$

But om' : M'I (plane mirror, object dis = Img dis)

$\therefore 30+\frac{10}{4}=M^{\prime }M+MI$

$\Rightarrow$ But $MI=23.2$ (given)

S0, $30+\frac{10}{4}=10-\frac{10}{4}+23,2$

$\Rightarrow \frac{20}{4}=03,2$

$\therefore \mu =\frac{20}{3,2}$

$\begin{array}{cc}\mu & =\frac{200}{128}\\ & =1.41\end{array}$