(A) For refraction at a spherical surface,the formula is: $\frac{\mu_2}{v} - \frac{\mu_1}{u} = \frac{\mu_2 - \mu_1}{R}$.Here,$\mu_1 = 1$ (air) and $\m

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(A) For refraction at a spherical surface,the formula is: $\frac{\mu_2}{v} - \frac{\mu_1}{u} = \frac{\mu_2 - \mu_1}{R}$.Here,$\mu_1 = 1$ (air) and $\mu_2 = 1.5$ (glass).According to the sign convention,the object distance $u = -PO = -x$ and the image distance $v = PI = x$,where $x$ is the distance $PO$.The radius of curvature $R$ is positive because the centre of curvature is in the glass medium.Substituting these values into the formula:$\frac{1.5}{x} - \frac{1}{-x} = \frac{1.5 - 1}{R}$$\frac{1.5}{x} + \frac{1}{x} = \frac{0.5}{R}$$\frac{2.5}{x} = \frac{0.5}{R}$$\frac{5}{2x} = \frac{1}{2R}$$x = 5R$.Therefore,the distance $PO$ is $5R$.

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

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$A$ spherical surface of radius of curvature $R$ separates air from glass (refractive index $= 1.5$). The centre of curvature is in the glass medium. $A$ point object $O$ is placed in air on the optic axis of the surface,so that its real image is formed at $I$ inside the glass. The line $OI$ intersects the spherical surface at $P$ and $PO = PI$. The distance $PO$ is equal to: (in $R$)

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A
$5$
B
$3$
C
$2$
D
$1.5$

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Refraction Through Single Curved Surface

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$A$ small object is enclosed in a transparent solid sphere of radius $8 \ cm$. The object is situated at $2 \ cm$ from the centre of the sphere. If its image appears to be at $3.2 \ cm$ from the nearest side,then the refractive index of the material of the sphere is:

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$A$ point object is kept at $P$ in front of a glass sphere of radius $R$. Its image is formed at $Q$ such that $PO = QO$. The refractive index of the material of the glass sphere is $1.4$. The distance $PO$ is equal to:

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Region $I$ and $II$ are separated by a spherical surface of radius $25\, \text{cm}$. An object is kept in region $I$ at a distance of $40\, \text{cm}$ from the surface. The distance of the image from the surface is $.....\, \text{cm}$.

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Explain the refraction by two transparent spherically curved surfaces.

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$A$ small object is enclosed in a transparent solid sphere of radius $8 \ cm$. The object is situated at $2 \ cm$ from the centre of the sphere. If its image appears to be at $3.2 \ cm$ from the nearest side,then the refractive index of the material of the sphere is:

$A$ point object is kept at $P$ in front of a glass sphere of radius $R$. Its image is formed at $Q$ such that $PO = QO$. The refractive index of the material of the glass sphere is $1.4$. The distance $PO$ is equal to:

Region $I$ and $II$ are separated by a spherical surface of radius $25\, \text{cm}$. An object is kept in region $I$ at a distance of $40\, \text{cm}$ from the surface. The distance of the image from the surface is $.....\, \text{cm}$.

Explain the refraction by two transparent spherically curved surfaces.

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