(B) The formula for refraction at a spherical surface is given by: $\frac{\mu_2}{v} - \frac{\mu_1}{u} = \frac{\mu_2 - \mu_1}{R}$.Here,$\mu_1 = 1$,$\mu

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$0.4 \ m$ to the left of the spherical surface

(B) The formula for refraction at a spherical surface is given by: $\frac{\mu_2}{v} - \frac{\mu_1}{u} = \frac{\mu_2 - \mu_1}{R}$.Here,$\mu_1 = 1$,$\mu_2 = 1.5$,$u = -0.2 \ m$ (object is placed to the left),and $R = +0.4 \ m$ (center of curvature is to the right).Substituting the values into the formula:$\frac{1.5}{v} - \frac{1}{-0.2} = \frac{1.5 - 1}{0.4}$$\frac{1.5}{v} + 5 = \frac{0.5}{0.4}$$\frac{1.5}{v} + 5 = 1.25$$\frac{1.5}{v} = 1.25 - 5$$\frac{1.5}{v} = -3.75$$v = \frac{1.5}{-3.75} = -0.4 \ m$.The negative sign indicates that the image is formed $0.4 \ m$ to the left of the spherical surface.

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

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$A$ spherical surface separates two media of refractive indices $1$ and $1.5$ as shown in the figure. Find the distance of the image of an object $O$ from the spherical surface. ($C$ is the center of curvature of the spherical surface and $R$ is the radius of curvature).

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A
$0.24 \ m$ to the right of the spherical surface
B
$0.4 \ m$ to the left of the spherical surface
C
$0.24 \ m$ to the left of the spherical surface
D
$0.4 \ m$ to the right of the spherical surface

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Ray Optics and Optical Instruments

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Refraction Through Single Curved Surface

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The figure shows a transparent sphere of radius $R$ and refractive index $\mu$. An object $O$ is placed at a distance $x$ from the pole of the first surface so that a real image is formed at the pole of the exactly opposite surface. If an object is placed at a distance $R$ from the pole of the first surface,then the real image is formed at a distance $R$ from the pole of the second surface. The refractive index $\mu$ of the sphere is given by

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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 $A$.

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$A$ spherical surface separates two media of refractive indices $1$ and $1.5$ as shown in the figure. Find the distance of the image of an object $O$ from the spherical surface. ($C$ is the center of curvature of the spherical surface and $R$ is the radius of curvature).

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$A$ spherical convex surface of power $5 \text{ dioptre}$ separates object and image space of refractive indices $1.0$ and $\frac{4}{3}$ respectively. The radius of curvature of the surface is (in $\text{ cm}$)

$A$ 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 $A$.

$A$ narrow parallel beam of light is incident paraxially on a solid transparent sphere of radius $r$ kept in air. What should be the refractive index if the beam is to be focused at the farther surface of the sphere?

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