Question

A plane mirror is made of glass slab $(n=1.5)2.5cm$ thick and silvered back. A point object placed $5cm$ in front the unsilvered face of the mirror. The position of final image is:

• A. $12cm$ from unsilured face
• B. $14.6cm$ from unsilvered face
• C. $5.67cm$ from unsilvered face
• D. $8.33cm$ from from unsilvered face

Answer 1

The correct option is D $8.33cm$ from from unsilvered face

$\begin{array}{c}\text{Let}{I}_1,I_2\text{and}{I}_3\text{be the image}\\ \text{formed by}\end{array}$

$\begin{array}{c}\text{(i) refraction from}ADC\\ \text{(ii) reflection from BEF.}\\ \text{(iii) Again refraction from ADC.}\\ \text{Then}B{I}_1=5n=5\left(1.5\right)=7.5\\ =7.5cm\\ \text{Now}ϵI_1=(7.5+2.5)cm=10cm\\ \in I_2=10cm\text{behind the mirror.}\end{array}$

$\begin{array}{c}\text{Now,}B{I}_2=10+2.5=12.5cm\\ \therefore B{I}_3=\frac{12.5}{\pi }=\frac{12.5}{1.5}\\ =8.33cm\\ \text{Hence,}D\text{is the correct answer}\end{array}$