(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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Ray Optics and Optical Instruments

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Refraction Through Single Curved Surface

$A$ parallel beam of light travelling in air (refractive index $1.0$) is incident on a convex spherical glass surface of radius of curvature $50 \ cm$. The refractive index of glass is $1.5$. The rays converge to a point at a distance $x \ cm$ from the centre of curvature of the spherical surface. The value of $x$ is . . . . . . $cm$.

MediumJEE MAIN 2026

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The slab of a material of refractive index $2$ shown in the figure has a curved surface $APB$ of radius of curvature $10 \, cm$ and a plane surface $CD$. On the left of $APB$ is air and on the right of $CD$ is water with refractive indices as given in the figure. An object $O$ is placed at a distance of $15 \, cm$ from the pole $P$ as shown. The distance of the final image of $O$ from $P$,as viewed from the left,is ..... $cm$.

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Light from a point source in air falls on a convex curved surface of radius $20 \,cm$ and refractive index $1.5$. If the source is located at $100 \,cm$ from the convex surface,the image will be formed at what distance from the object?

DifficultJEE MAIN 2024

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$A$ quarter cylinder of radius $R$ and refractive index $1.5$ is placed on a table. $A$ point object $P$ is kept at a distance of $mR$ from it. Find the value of $m$ for which a ray from $P$ will emerge parallel to the table as shown in the figure.

Difficult

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An air bubble in a glass sphere $(\mu=1.5)$ is situated at a distance $3\; cm$ from a convex surface of diameter $10\; cm$. At what distance from the surface will the bubble appear (in $; cm$)?

Medium

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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

Light from a point source in air falls on a convex curved surface of radius $20 \,cm$ and refractive index $1.5$. If the source is located at $100 \,cm$ from the convex surface,the image will be formed at what distance from the object?

$A$ quarter cylinder of radius $R$ and refractive index $1.5$ is placed on a table. $A$ point object $P$ is kept at a distance of $mR$ from it. Find the value of $m$ for which a ray from $P$ will emerge parallel to the table as shown in the figure.

An air bubble in a glass sphere $(\mu=1.5)$ is situated at a distance $3\; cm$ from a convex surface of diameter $10\; cm$. At what distance from the surface will the bubble appear (in $; cm$)?

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