Mirror Formula for Spherical Mirrors Questions

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Very Short Answers Questions [1 Mark Questions]

Ques. What is a spherical mirror?

Ans. A spherical mirror is a reflecting surface that is formed by a part of a hollow sphere. These are of two types

• Concave mirror
• Convex mirror

Ques. What is the focal length of a spherical mirror?

Ans. The distance between the pole and the principal focus of the spherical mirror is called the focal length of the spherical mirror.

Ques. What is the principal axis of a spherical mirror?

Ans. The line joining the center of the curve and the pole of the spherical mirror is called the principal axis of a spherical mirror.

Ques. What is the refraction of the light?

Ans. Refraction is the bending of light as it moves from one transparent material into another transparent one.

Ques. What is the reflection of the light?

Ans. The phenomenon of bouncing back of the light to the same medium after striking a smooth surface is known as the reflection of light.

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Short Answers Questions [2 Marks Questions]

Ques. What is the mirror formula for a spherical mirror?

Ans. The mirror equation, commonly referred to as the mirror formula, describes the relationship between the object's distance from the mirror, the focal length of the mirror, and the image's distance from the mirror.

The mirror formula for a spherical mirror is given by

1/u + 1/v = 1/f

Where

• f is the focal length of the spherical mirror
• u is the distance of the object from the mirror
• v is the distance of the image from the mirror

Ques. What is the magnification formula of a spherical mirror?

Ans. The magnification formula of a spherical mirror is given by

m = Height of the image (h’) / Height of the object (h)

In terms of object and image distance from the spherical mirror, the magnification formula is given by

m = – v/u

Where

• v is the distance of the image from the mirror
• u is the distance of the object from the mirror

Ques. Where can we use the mirror formula?

Ans. The mirror formula of a spherical mirror is used to determine the image size, magnification value, and distance between the image and the spherical mirror.

Ques. Write the formula for the magnification of a spherical mirror in terms of object distance, image distance, and focal length of the mirror.

Ans. Let u and v be the distance of the object and image respectively from the spherical mirror. If f is the focal length of the mirror, then the magnification of the spherical mirror is given by

m = f/(f-u) = (f-v)/f

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Long Answers Questions [3 Marks Questions]

Ques. If half of the reflecting surface of a concave mirror is painted black, then what will happen to the image formed by the mirror?

Ans. Every part of the mirror forms a complex image of an object. 

• The brightness of the final image depends upon the light reflected by the mirror. 
• When half of the reflecting surface of a concave mirror is painted black, the size of the image will be the same.
• However, the brightness or intensity of the image reduces to almost half because the aperture of the exposed part of the concave mirror decreases.

Ques. Define sign convention rules for spherical mirrors.

Ans. The sign convention rules used for spherical mirrors are

• All the distances are measured from the pole of a spherical mirror.
• Distances measured in the direction of the incident light are taken as positive, whereas the distances measured in the direction opposite to that of the incident light are taken as negative.
• The upward distances perpendicular to the principal axis are taken as positive while the downward distances perpendicular to the principal axis are taken as negative.

Ques. What are the uses of spherical mirrors?

Ans. Spherical mirrors are classified into two types: convex and concave mirrors.

Convex Mirror Applications

• Vehicle mirrors as rear-view mirrors.
• Used in a magnifying glass.
• As security mirrors.
• Reflectors for street lights.
• A telescope uses convex mirrors.
• Convex mirrors are used in the making of a sunglass lens.

Concave Mirror Applications

• Headlights
• Solar furnaces
• Shaving mirrors
• Astronomical telescopes
• Dental mirrors
• Ophthalmoscope
• Head mirrors
• Satellite dishes

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Very Long Answers Questions [5 Marks Questions]

Ques. An object is placed (i) 10 cm (ii) 5 cm in front of a concave mirror of radius of curvature 15 cm. Compare the position, nature, and magnification of the image in each case.

Ans. Given that the radius of curvature of the concave mirror is, R = - 15 cm.

Therefore, its focal length will be, f = -15/2 cm

Case (i): When the object is placed 10 cm in front of the concave mirror, i.e. u = - 10 cm

Using the mirror formula for spherical mirrors, we have

1/f = 1/u + 1/v

Where v is the distance of the image from the mirror.

On substituting the values, we get

-2/15 = – 1/10 + 1/v

⇒ 1/v = – 2/15 + 1/10

⇒ v = – 30 cm

Now magnification is given by

m = -v/u = - (-30/-10) = -3

Hence, the image is on the same side as the object, and the image is real, inverted, and magnified.

Case (ii): When the object is placed 5 cm in front of the concave mirror, i.e. u = - 5 cm

Using the mirror formula for spherical mirrors, we have

1/f = 1/u + 1/v

Where v is the distance of the image from the mirror.

On substituting the values, we get

-2/15 = -1/5 + 1/v

⇒ 1/v = – 2/15 + 1/5

⇒ v = 15 cm

Now magnification is given by

m = – v/u = - (15/-5) = 3

Hence, the image formed behind the mirror, and is virtual, erect, and magnified.

Ques. A square of side 4.0 cm is placed 20 cm away from the concave mirror of radius of curvature 30 cm. Calculate the area enclosed by the image of the square.

Ans. Given

• The height of the square, h = 4 cm
• Distance of the square from the concave mirror, u = -20 cm
• The radius of curvature of the mirror, R = – 30 cm

The focal length of the mirror is given by

f = R/2 = – 30/2 = -15 cm

Using the mirror formula for spherical mirrors, we have

1/f = 1/u + 1/v

Where v is the distance of the image from the mirror.

On substituting the values, we get

-1/15 = – 1/20 + 1/v

⇒ 1/v = – 1/15 + 1/20

⇒ v = – 60 cm

Now magnification is given by

m = – v/u = - (-60/-20) = -3

Here the negative sign on the magnification shows that the image is real.

Also. magnification is given by

m = height of the image(h’) / height of the object(h)

On substituting the values, we get

-3 = h’/4

⇒ h’ = -12 cm

Hence, the area of the image is 12 x 12 = 144 cm²

Ques. Derive the relationship between the speed of an object and the speed of the image formed by a spherical mirror.

Ans. The mirror formula for a spherical mirror is given by

1/u + 1/v = 1/f …(i)

Where

• f is the focal length of the spherical mirror
• u is the distance of the object from the mirror
• v is the distance of the image from the mirror

On differentiating the above equation with respect to time, we get

-1/u² du/dt - 1/v² dv/dt = 0

The differentiation of focal length (f) with respect to time is zero because the focal length of the spherical mirror is constant.

⇒ 1/v² dv/dt = 1/u² du/dt

⇒ dv/dt = – v²/u² du/dt

Here

• dv/dt = v_i i.e. the speed of the image, and
• du/dt = v₀ i.e. the speed of the object

On substituting, we get

v_i = – (u/v)² v₀

From equation (i), we get v = uf/(u-f), Hence

Speed of the image is given by

v_i = – \([\frac{f}{u-f}]^2v_0\)

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