(D) The refraction formula for a spherical surface is given by $\frac{\mu_2}{v} - \frac{\mu_1}{u} = \frac{\mu_2 - \mu_1}{R}$.For figure $A$,the object

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(D) The refraction formula for a spherical surface is given by $\frac{\mu_2}{v} - \frac{\mu_1}{u} = \frac{\mu_2 - \mu_1}{R}$.For figure $A$,the object distance $u = -x$ and the radius of curvature $R$ is positive $(+R)$.Substituting these values: $\frac{\mu_2}{v} = \frac{\mu_2 - \mu_1}{R} - \frac{\mu_1}{x} = \frac{x(\mu_2 - \mu_1) - R\mu_1}{xR}$.For a virtual image,$v Since $x, R > 0$,we must have $x(\mu_2 - \mu_1) - R\mu_1 Case $1$: If $\mu_2 0$. Thus,a virtual image is always formed if $\mu_2 Case $2$: If $\mu_2 > \mu_1$,then $x Therefore,both statements $(A)$ and $(B)$ are correct.

Class 12 Physics Ray Optics and Optical Instruments Refraction Through Single Curved Surface

$A$ curved surface of radius $R$ separates two media of refractive indices $\mu_1$ and $\mu_2$ as shown in figures $A$ and $B$. Choose the correct statement$(s)$ related to the virtual image formed by object $O$ placed at a distance $x$,as shown in figure $A$.

A
Virtual image is formed for any position of $O$ if $\mu_2 < \mu_1$.
B
Virtual image can be formed if $x > R$ and $\mu_2 < \mu_1$.
C
Virtual image is formed if $x < R$ and $\mu_2 > \mu_1$.
D
Both $(A)$ and $(B)$.

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Class 12

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Ray Optics and Optical Instruments

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Refraction Through Single Curved Surface

$A$ spherical interface of radius $R$ separates two media of refractive indices $1$ and $1.4$ respectively, as shown in the figure below. $A$ point source is placed at a distance of $4R$ in front of the spherical interface. The magnitude of the lateral magnification of the point source image is . . . . . . .

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What is the focal length of this curved surface in $cm$?

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$A$ spherical vessel of radius $10 \, cm$ is filled with water of refractive index $\mu = 4/3$. $A$ fish is at a distance of $4 \, cm$ from the center as shown in the figure. If viewed from end $E$,at what distance will the fish appear to be (in $, cm$)? (Neglect the thickness of the vessel)

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Light from a point source in air falls on a convex spherical glass surface $(\mu = 1.5, R = 20 \, cm)$. The distance of the light source from the glass surface is $100 \, cm$. At what position is the image formed (in $, cm$)?

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In the figure shown here,a point object $O$ is placed in air. $A$ spherical boundary separates various media with a radius of curvature $2.0 \, m$. $AB$ is the principal axis. The refractive index above $AB$ is $1.6$ and below $AB$ is $2.0$. The separation between the images formed due to refraction at the spherical surface is

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$A$ curved surface of radius $R$ separates two media of refractive indices $\mu_1$ and $\mu_2$ as shown in figures $A$ and $B$. Choose the correct statement$(s)$ related to the virtual image formed by object $O$ placed at a distance $x$,as shown in figure $A$.

Similar Questions

What is the focal length of this curved surface in $cm$?

$A$ spherical vessel of radius $10 \, cm$ is filled with water of refractive index $\mu = 4/3$. $A$ fish is at a distance of $4 \, cm$ from the center as shown in the figure. If viewed from end $E$,at what distance will the fish appear to be (in $, cm$)? (Neglect the thickness of the vessel)

Light from a point source in air falls on a convex spherical glass surface $(\mu = 1.5, R = 20 \, cm)$. The distance of the light source from the glass surface is $100 \, cm$. At what position is the image formed (in $, cm$)?

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