Mirror Equation Important Questions

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Very Short Answer Questions [1 Mark Questions]

Ques. What is mirror formula

1. 1/f = 1/u - 1/v
2. 1/v = 1/u + 1/f
3. 1/f = 1/u x 1/v
4. 1/f = 1/u + 1/v

Ans. The correct answer is d. 1/f = 1/u + 1/v

Explanation: The mirror formula shows the relationship between the image distance, the object distance, and the focal length of the spherical mirror. It is given by

1/f = 1/u + 1/v

Ques. How is focal length related to the radius of curvature?

1. f = R/2
2. f = 2/R
3. R = f/2
4. R = 2/f

Ans. The correct answer is a. f = R/2

Explanation: The focal length (f) of a spherical mirror is equal to half of the radius of curvature (R) i.e. 

f = R/2

Ques. The distance between the pole of the mirror and the object is known as

1. Focal distance
2. Object distance
3. Focal Length
4. Object height

Ans. The correct answer is b. Object distance

Explanation: Object distance is defined as the distance between the pole of the mirror and the location of the object.

Ques. If the distance of the object from a concave mirror is 4 times the focal length, the position of the image will be obtained at

1. v = 4f
2. v = – 4f/3
3. v = – 3f/4
4. v = f/4

Ans. The correct answer is b. v = – 4f/3

Explanation: Given, u = – 4f (Using sign convention)

From mirror formula, we have

1/f = 1/u + 1/v

⇒ 1/v = 1/f - 1/u

⇒ 1/v = 1/f - (-1/4f) = – 3f/4

⇒ v = – 4f/3

Ques. Mirror equation holds good for

1. Plane mirror
2. Convex mirror
3. Concave mirror
4. Concave and convex mirror

Ans. The correct answer is d. Concave and convex mirror

Explanation: The mirror formula is valid for all types of spherical mirrors as well as every possible position in which an object can reside.

Ques. The ray that is 90° to the surface, or the ray that is perpendicular to the reflecting surface is called

1. Incident ray
2. Normal ray
3. Refracted ray
4. Reflected ray

Ans. The correct answer is b. Normal ray

Explanation: An imaginary ray passing perpendicular to the plane of the reflecting surface is known as the normal ray.

Ques. The angle formed between the normal and the incident ray at the point of incidence is known as

1. The angle of reflection
2. The angle of interference
3. The angle of refraction
4. The angle of incidence

Ans. The correct answer is d. The angle of incidence

Explanation: The angle formed by the incident ray of light and normal to the surface is known as the angle of incidence.

Ques. The angle formed between the normal and the reflected ray is known as

1. The angle of refraction
2. The angle of reflection
3. The angle of interference
4. The angle of incidence

Ans. The correct answer is b. The angle of reflection

Explanation: The angle formed by the reflected ray of light and normal to the surface is known as the angle of reflection.

Ques. A concave mirror is held in water. What should be the change in the focal length of the mirror?

1. Remains the same
2. Doubled
3. Halved
4. Increases exponentially

Ans. The correct answer is a. Remains the same

Explanation: The focal length of a concave mirror is independent of the medium. As a result, even after holding the mirror in water, the focal length will remain constant.

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Short Answer Questions [2 Marks Questions]

Ques. What are the various types of mirrors?

Ans. There are three types of mirrors

• Plane mirror
• Concave mirror
• Convex mirror

Ques. What is a mirror equation?

Ans. The mirror equation is a relation between the distance of the object, the distance of the image, and the focal length of a spherical mirror.

It is given by

1/f = 1/u + 1/v

Where

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

Ques. What is the reflection of light?

Ans. The reflection of light is the phenomenon of bouncing of light to the same medium when the light falls on a surface.

Ques. What are the different types of reflection?

Ans. The different types of reflection are

• Regular reflection or specular reflection
• Diffused reflection
• Multiple reflection

Ques. What is diffuse reflection?

Ans. Diffuse reflection is the reflection of light, other waves, or particles of a surface in such a way that a ray incident on the surface is scattered at many different angles rather than just one, as in specular reflection.

Ques. Define the principle of reversibility of light.

Ans. According to the principle of reversibility of light, if the path of a ray of light is reversed after suffering many reflections and refractions, it retraces its path.

Ques. Define absolute refractive index.

Ans. The absolute refractive index is defined as the ratio of the speed of light in air or vacuum to the speed of light in the medium i.e.

Absolute refractive index, µ = (speed of light in air or vacuum)/(speed of light in the medium)

⇒ µ = c/v

Ques. Define the focal plane of a spherical mirror.

Ans. A line passing through the principal focus and perpendicular to the principal axis on which the rays of light coming from distant objects making different angles with the principal axis converge or diverge is known as the focal plane.

Ques. What is the nature of the image formed by a plane mirror?

Ans. The image formed by the plane mirror is virtual, erect, inverted, and the same size as that of the object

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Long Answer Questions [3 Marks Questions]

Ques. An object is placed at a distance of 40 cm from a concave mirror of a focal length of 15 cm. If the object is displaced through a distance of 20 cm towards the mirror, what will be the displacement of the image?

Ans. Given

• The distance of the object, u = – 40 cm
• The focal length of the concave mirror, f = – 15 cm

From the mirror formula, we have

1/f = 1/u + 1/v

⇒ 1/v = 1/f - 1/u

On substituting the values, we get

1/v = (-1/15) - (-1/40)

⇒ v = – 24 cm

If the object is displaced through 20 cm, then the new object distance will be

u’ = – 40 + 20 = – 20 cm

Using the mirror formula, the new distance of the image will be

1/v’ = (-1/15) - (-1/20)

⇒ v’ = – 60 cm

Displacement of the image, (v’ - v) = -60 - (-24) = – 36 cm

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 any spherical mirror is given by

1/u + 1/v = 1/f …(i)

Where

• f is the focal length
• u is the object distance
• v is the image distance

On differentiating the above equation time t, we get

-1/u² du/dt - 1/v² dv/dt = 0

The differentiation of focal length (f) with 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

The speed of the image is given by

\(v_i= – [\frac{f}{u -f}]^2v_0\)

Ques. What are the uses of spherical mirrors?

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

Convex Mirror Applications

• It is used in vehicle mirrors as rear-view mirrors.
• It is used as a reflector for street lights.
• It is used in a magnifying glass.
• A telescope uses convex mirrors.
• It is used as a security mirror.
• 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

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 light entering are considered positive, whereas distances observed in the opposite direction are considered negative.
• The upward distances perpendicular to the principal axis are considered positive, whereas the downward distances are considered negative.

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Very Long Answer Questions [5 Marks Questions]

Ques. Derive mirror formula for a concave mirror.

Ans. Let AB be an object lying on the principal axis of the concave mirror.

A’B’ is the real image of the object AB.

△ABC and △A’B’C are similar, therefore

A’B’/AB = CA’/CA …(i)

Also, △ABP and △A’B’P are similar, therefore

A’B’/AB = PA’/PA …(ii)

From equation (i) and (ii), we get

CA’/CA = PA’/PA …(iii)

As per the sign convention, all the distances are measured from the pole, therefore

CA’ = (PC - PA’) and CA = (PA - PC)

Substituting the above values in the equation (iii), we get

(PC - PA’)/(PA - PC) = PA’/PA

Applying sign convention

• PA’ = -v
• PC = -R
• PA = -u

Thus, (-R + v)/(-u + R) = (-v/-u)

⇒ uR - uv = uv - vR

⇒ uR + vR = 2uv

Dividing the above equation by uvR, we get

1/v + 1/u = 2/R

But R = 2f

⇒ 1/v + 1/u = 1/f

The above equation is the mirror formula for the concave mirror when the real image of an object i formed.

Ques. A 2.0 cm tall object is placed 15 cm in front of a concave mirror of a focal length of 10 cm. What is the size and nature of the image?

Ans. According to the cartesian sign convention

• Distance of the object, u = -15 cm
• The focal length of the concave mirror, f = -10 cm
• Height of the object, h = 2 cm

According to the mirror formula, we have

1/f = 1/u + 1/v

⇒ 1/v = 1/f - 1/u

On substituting the values, we get

1/v = -1/10 - (-1/15)

⇒ v = -30 cm

The negative sign shows that the image is formed 30 cm from the mirror on the same side of the object. Therefore it is a real image.

Magnification of the mirror is given by

m = -v/u = h’/h

Where h’ is the height of the image.

On substituting the value of v, u, and h using sign conventions, we get

m = -(-30/-15) = h’/2

⇒ h’ = -4 cm

The negative sign shows that the image is inverted.

Hence the image is real, inverted, and of size 4 cm at a distance of 30 cm in front of the mirror.

Ques. An object moving at a speed of 5 m/s towards a concave mirror of focal length f = 1 m is at a distance of 9 m. What is the average speed of the image?

Ans. Given

• The focal length of the concave mirror, f = - 1 m
• The distance of the object, u = - 9 m

According to the mirror formula, we have

1/f = 1/v + 1/u

⇒ 1/v = 1/f - 1/u

On substituting the values, we get

1/v = (-1/1) - (-1/9)

⇒ 1/v = -1 + (1/9) = -8/9

⇒ v = -9/8 m

As the object moves at a constant speed of 5 m/s after 1 second the position of the object is

u’ = -9 m + 5 m = -4 m

Hence, the position of the image after 1 second is

1/v’ = 1/f - 1/u’

⇒ 1/v’ = (-1/1) - (-1/4)

⇒ v’ = -4/3 m

The shift in the position of the image in 1 second is

v - v’ = (-9/8) - (-4/3)

⇒ v - v’ = 1/5 m = 0.2 m

Hence the average speed of the image is 0.2 m/s

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