Mirror Formula Formal Proof

Q. A small candle, $2.5\text{cm}$ in size is placed at $27\text{cm}$ in front of a concave mirror of radius of curvature $36\text{cm}$. At what distance from the mirror should a screen be placed in order to obtain a sharp image? Describe the nature and size of the image. If the candle is moved closer to the mirror, how would the screen have to be moved?

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If an object of $7cm$height is placed at a distance of $12cm$from a convex lens of focal length$8cm$, find the position, nature and height of the image.

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A converging lens has focal length of $12cm$, Calculate at what distance should the object be placed from the lens so that it forms an image at $48cm$ on the other side of the lens.

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A concave mirror has a focal length of 20 cm. Find the position or positions of an object for which the image-size is double of the object - size.

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A divergent lens has a focal length of $20cm$. At what distance should an object of height $4cm$ from the optical centre of the lens be placed so that its image is formed $10cm$ away from the lens. Find the size of the image also.

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An object is kept at a distance of $4m$ in front of a spherical mirror which forms its erect image at a distance of$1.0m$ from the mirror. What is the magnification? Is the mirror concave or convex?

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Two thin lenses of power $+2.0D$ and $-1.5D$ are placed in contact. Find the a. power and b. focal length of the combination of lenses. c. Also state the nature of the lens formed by the combination of these lenses.

Q. The image of a small electric bulb fixed on the wall of a room is to be obtained on the opposite wall 3𝑚 away by means of a large convex lens. What is the maximum possible focal length of the lens required for the purpose?

Q. The speed of light in media $M_1$ and $M_2$ is $1.5\times {10}^8\text{m/s}$ and $2.0\times {10}^8\text{m/s}$ respectively. A ray of light enters from medium $M_1$ to $M_2$ at an incidence angle $i$. If the ray suffers total internal reflection, the value of $i$ is

1. equal to or less than ${\sin }^{-1}\left(\frac{3}{5}\right)$
2. less than ${\sin }^{-1}\left(\frac{2}{3}\right)$
3. equal to ${\sin }^{-1}\left(\frac{2}{3}\right)$
4. equal to or greater than ${\sin }^{-1}\left(\frac{3}{4}\right)$

Q.

A converging lens has a focal length $40cm$. Calculate its power.

Q.

The far point of a myopic person is $150cm$ in front of the eye. Calculate the focal length and power of the lens required to enable him to see distant objects clearly.

Q. A screen is placed 90 𝑐𝑚 from an object. The image of the object on the screen is formed by a convex lens at two different locations separated by $20\text{cm}$. Determine the focal length of the lens.

Q.

An object is placed at a distance of X from a convex lens, when a real image is formed at a distance of$15cm$ from the lens. If the focal length of the lens is$10cm$, calculate (a) value of X (b) the magnification produced. State the characteristics of the image.

Q. A child and a man are standing in front of a plane mirror as shown in the figure. What should be the minimum height of the mirror so that the child can completely see his/her own image as well as the man's image in the mirror.

1. $\frac{H}{2}$
2. $\frac{H}{6}$
3. $\frac{3H}{2}$
4. $\frac{5H}{6}$

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A lens has a power of $-4D$. What is the nature and focal length of the lens?

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If the power of a lens is $+5$ dioptre, what is its focal length?

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A concave mirror is used as a shaving glass. Give reason.

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For a plane mirror, the magnification (M = +1). What does this signify for (a) M=1 (b) positive sign of M?

Q. A prism is made of glass of unknown refractive index. A parallel beam of light is incident on a face of the prism. The angle of minimum deviation is measured to be ${40}^{\circ }$. What is the refractive index of the material of the prism? The refracting angle of the prism is 60°. If the prism is placed in water (refractive index 1.33), predict the new angle of minimum deviation of a parallel beam of light.

Q. A jar of height $h$ is filled with a transparent liquid of refractive index $\mu$ (Figure). At the centre of the jar on the bottom surface is a dot. Find the minimum diameter of a disc, such that when placed on the top surface symmetrically about the centre, the dot is invisible.

Q.

Name the spherical mirror which always forms a virtual image of an object.

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How is the power of a combination of lenses described? The powers of the lenses are $P_1,P_2,P_3$ and $P_4$.

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An object $3.0cm$ high is placed perpendicular to the principal axis of a concave lens of focal length $15.0cm$. The image is formed at the distance of $10.0cm$ from the lens. Calculate a. the distance of object placed and b. size and nature of image formed.

Q. An astronomical refractive telescope has an objective of focal length 20 𝑚 and an eyepiece of focal length 2 𝑐𝑚.

1. The image formed is inverted.
2. The length of the telescope tube is " 20.02 𝑚.
3. The magnitude of magnification is 1000.
4. An objective of a larger aperture will increase the brightness and reduce chromatic aberration of the image.

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A concave lens of focal length $20cm$ forms an image at a distance of $10cm$ from the lens. What is the distance of the object from the lens.

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A hypermetropic person has $75cm$ as his near point. What will be the focal length and power of the convex lens in his spectacles?

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How is the sign of the magnification related to the nature of image formed by the mirror?

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Define magnification produced by a mirror.

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The refractive index of crown glass is $1.52$. What is the meaning of this statement?

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A clock is hung on a wall has marks instead of number on its dial. On the opposite wall there is a mirror and image of mirror in the clock is read and it indicates the time as 8:20.The time in the clock is__________