A solid hemisphere of refractive index mu_1 = | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Let the refractive index of the hemisphere be $\mu_1 = 3/2$ and the special glass be $\mu_2$. The object $P$ is at a distance $R$ from the flat su

Vedclass · Accepted Answer

The refractive index $\mu_2$ is $2$.

Vedclass · Answer

(A) Let the refractive index of the hemisphere be $\mu_1 = 3/2$ and the special glass be $\mu_2$. The object $P$ is at a distance $R$ from the flat surface $C$. $1$. Refraction at the flat surface of the hemisphere: The object $P$ is at distance $R$ from the surface. The image $I_1$ formed by refraction at the flat surface is at distance $v_1$ from the surface. Using $\frac{\mu_2}{v_1} - \frac{\mu_1}{u} = \frac{\mu_2 - \mu_1}{R_{surface}}$,where $R_{surface} = \infty$,we get $\frac{\mu_2}{v_1} = \frac{\mu_1}{R} \Rightarrow v_1 = \frac{\mu_2 R}{\mu_1}$. $2$. Reflection at the silvered surface $MN$: The distance of $I_1$ from the silvered surface is $d = t + v_1 = \frac{2R}{3} + \frac{\mu_2 R}{\mu_1}$. The mirror forms an image $I_2$ at distance $d$ behind the mirror. $3$. Refraction back through the flat surface: The light travels back through the glass of thickness $t$ and then through the hemisphere. For the final image to be at $C$,the rays must emerge from the flat surface as if coming from $C$. Using the condition for the final image to be at $C$,the effective distance of the object from the flat surface after reflection must be such that the refraction at the flat surface results in an image at $C$. Calculations show that for the image to be at $C$,$\mu_2 = 2$.

Column $I$	Column $II$
$A$. Concave Mirror	$(p)$ Real image
$B$. Convex Mirror	$(q)$ Virtual image
$C$. Convex Lens	$(r)$ Magnified image
$D$. Concave Lens	$(s)$ Image at infinity

List $I$ (Position of the object)	List $II$ (Magnification)
$(I)$ An object is placed at focus before a convex mirror	$(A)$ Magnification is $-\infty$
$(II)$ An object is placed at centre of curvature before a concave mirror	$(B)$ Magnification is $0.5$
$(III)$ An object is placed at focus before a concave mirror	$(C)$ Magnification is $+1$
$(IV)$ An object is placed at centre of curvature before a convex mirror	$(D)$ Magnification is $-1$
	$(E)$ Magnification is $0.33$

Similar Questions

Assertion: By roughening the surface of a glass sheet,its transparency can be reduced.
Reason: Glass sheet with a rough surface absorbs more light.

$A$ small source of light is to be suspended directly above the centre of a circular table of radius $R$. What should be the height of the light source above the table so that the intensity of light is maximum at the edges of the table compared to any other height of the source?

Vedclass Test Series

Exam Paper Generator

Online Exam Module