(D) The total deviation $\delta$ produced by two plane mirrors inclined at an angle $\theta$ is given by $\delta = 360^o - 2\theta$.Given $\delta = 24

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(D) The total deviation $\delta$ produced by two plane mirrors inclined at an angle $\theta$ is given by $\delta = 360^o - 2\theta$.Given $\delta = 240^o$,we have $240^o = 360^o - 2\theta$,which implies $2\theta = 120^o$,so $\theta = 60^o$.Thus,option $A$ is correct.For the number of images $n$,we calculate $m = 360^o / \theta = 360^o / 60^o = 6$.If $m$ is an even integer,the number of images $n = m - 1$ regardless of whether the object is placed symmetrically or unsymmetrically.Therefore,$n = 6 - 1 = 5$.Since both options $B$ and $C$ are correct,option $D$ is the correct choice.

Class 12 Physics Ray Optics and Optical Instruments Mix Examples-Ray Optics

Two plane mirrors are at an angle such that a ray incident on one mirror undergoes a total deviation of $240^o$ after two reflections. Which of the following statements is correct?

A
The angle between the mirrors is $60^o$.
B
The number of images formed by this system will be $5$,if an object is placed symmetrically between the mirrors.
C
The number of images will be $5$ if an object is kept unsymmetrically between the mirrors.
D
All of the above.

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Ray Optics and Optical Instruments

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Mix Examples-Ray Optics

To find the focal length of a convex mirror,a student records the following data:

Object Pin Convex Lens Convex Mirror Image Pin

$22.2 \, cm$ $32.2 \, cm$ $45.8 \, cm$ $71.2 \, cm$

The focal length of the convex lens is $f_1$ and that of the mirror is $f_2$. Taking index correction to be negligibly small,$f_1$ and $f_2$ are close to:

Object Pin	Convex Lens	Convex Mirror	Image Pin
$22.2 \, cm$	$32.2 \, cm$	$45.8 \, cm$	$71.2 \, cm$

DifficultJEE MAIN 2016

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$A$ point source of light moves in a straight line parallel to a plane table. Consider a small portion of the table directly below the line of movement of the source. The illuminance $E$ at this portion varies with its distance $r$ from the source as:

Easy

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$A$ bulb of $100 \text{ W}$ is hanging at a height of $1 \text{ m}$ above the centre of a circular table of diameter $4 \text{ m}$. If the intensity at a point on its rim is $I_0$,then the intensity at the centre of the table will be:

Difficult

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Ray optics is valid when characteristic dimensions are:

EasyAIPMT 1994

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$A$ glass sphere of refractive index $1.5$ and radius $40\,cm$ has half its hemispherical surface silvered. The point where a parallel beam of light,coming along a diameter,will focus (or appear to) after coming out of the sphere,will be:

Difficult

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Two plane mirrors are at an angle such that a ray incident on one mirror undergoes a total deviation of $240^o$ after two reflections. Which of the following statements is correct?

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$A$ point source of light moves in a straight line parallel to a plane table. Consider a small portion of the table directly below the line of movement of the source. The illuminance $E$ at this portion varies with its distance $r$ from the source as:

$A$ bulb of $100 \text{ W}$ is hanging at a height of $1 \text{ m}$ above the centre of a circular table of diameter $4 \text{ m}$. If the intensity at a point on its rim is $I_0$,then the intensity at the centre of the table will be:

Ray optics is valid when characteristic dimensions are:

$A$ glass sphere of refractive index $1.5$ and radius $40\,cm$ has half its hemispherical surface silvered. The point where a parallel beam of light,coming along a diameter,will focus (or appear to) after coming out of the sphere,will be:

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