Physics Class 12 NCERT Solutions: Chapter 9 Ray Optics and Optical Instruments Part 1

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Mirror Formula of concave mirror

Mirror Formula of Concave Mirror

Mirror Formula of concave mirror

Q: 1. A small candle, in size is placed at in front of a concave mirror of radius of curvature . 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?

Answer:

Size of the candle,

Image size

Object distance,

Radius of curvature of the concave mirror,

Focal length of the concave mirror,

Image distance

The image distance can be obtained using the mirror formula:

Therefore, the screen should be placed away from the mirror to obtain a sharp image.

The magnification of the image is given as:

The height of the candle’s image is . The negative sign indicates that the image is inverted and real.

If the candle is moved closer to the mirror, then the screen will have to be moved away from the mirror in order to obtain the image.

Q: 2. A needle is placed away from a convex mirror of focal length . Give the location of the image and the magnification. Describe what happens as the needle is moved farther from the mirror.

Answer:

Height of the needle,

Object distance,

Focal length of the convex mirror,

Image distance

The value of v can be obtained using the mirror formula:

Hence, the image of the needle is away from the mirror. Also, it is on the other side of the mirror.

The image size is given by the magnification formula:

Hence, magnification of the image,

The height of the image is . The positive sign indicates that the image is erect, virtual, and diminished.

If the needle is moved farther from the mirror, the image will also move away from the mirror, and the size of the image will reduce gradually.

Q: 3. A tank is filled with water to a height of . The apparent depth of a needle lying at the bottom of the tank is measured by a microscope to be . What is the refractive index of water? If water is replaced by a liquid of refractive index up to the same height, by what distance would the microscope have to be moved to focus on the needle again?

Answer:

Actual depth of the needle in water,

Apparent depth of the needle in water,

Refractive index of water

The value of can be obtained as follows:

Hence, the refractive index of water is about .

Water is replaced by a liquid of refractive index,

The actual depth of the needle remains the same, but its apparent depth changes. Let y be the new apparent depth of the needle. Hence, we can write the relation:

Hence, the new apparent depth of the needle is . It is less than . Therefore, to focus the needle again, the microscope should be moved up.

∴Distance by which the microscope should be moved up