Question

One face of a rectangular glass plate $6\,Cm$ thick is silvered. An object held $8\,Cm$ in front of the fist face, forms an image $12\,Cm$ behind the silvered face. The refractive index of the glass is:
A. 1.2
B. $1.6$
C. $1.5$
D. $1.3$

Answer 1

Hint In the question, the thickness of one of the faces of the rectangular plate is given and the second face of the dimensions is given. By finding the apparent faces of the mirror, then we substitute the known values in the expression of the refractive index, we get the value of the refractive index of the glass.
Formula used:
The expression for finding the refractive index of the glass is
$\mu = \dfrac{{{\text{Real Depth}}}}{{{\text{Apparent Depth}}}}$

Complete step by step answer
Given that,
Thickness of the glass plate, $t = 6\,cm.$
Distance of the object, $u = 8\,cm.$
Distance of the image behind the silvered face, $v = 12\,cm.$
Let x be the apparent position of the silvered surface in terms of centimeter,
Therefore, Distance of object from the mirror $=$ Distance of image from the mirror.
So, we written the expression as
$x + 8 = 12 + 6 - x$
Performing the arithmetic operations in the above equation, we get
$x = 5\,cm.$
Now, we have to find the refractive index of the glass, we get
Refractive index of the glass is the ratio of the real depth of the mirror to the apparent depth of the mirror.
$\mu = \dfrac{{{\text{Real Depth}}}}{{{\text{Apparent Depth}}}}$
From the question, Real depth $= 6\,cm.$
Substitute the values in the above equation, we get
$\mu = \dfrac{6}{5}$
Simplify the equation, we get
$\mu = 1.2$
Therefore, the refractive index of the glass is 1.2.

Hence, from the above options, option A is correct.

Note In the question, the value of the actual depth of the mirror is given. we know that apparent depth which means the image is formed due to reflection of the silvered face by the one end of the face through the surface of the mirror. After getting those values, substitute in the equation of the refractive index then we will get the result.