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A convex mirror is a spherical mirror wherein the reflective surface bulges out towards the source of light. A convex mirror reflects the light outwards and is therefore not used to focus light. The image appears smaller than the object projected, however, gets larger as this object approaches the convex mirror. They are also referred to as the fish eye mirror or diverging mirror
Key Terms: Spherical Mirror, Concave and Convex Mirror, Converging Mirror, Convex Car Mirror, Rear View Convex Mirror
What are Convex Mirrors?
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Convex Mirror is a curved mirror in which the reflective surface bulges toward the light source. The bulging side is responsible for reflecting the light outwards and is not used to focus light.
- Since these mirrors have the ability to reflect all the light that falls on them, convex mirrors always form imaginary or virtual images.
- Since convex mirrors always form imaginary or virtual images, the size of the image will always be smaller than the actual size of the object.
- Therefore, these mirrors are used in places where the images of the objects have to be seen in a smaller size.
Convex mirrors
The focal point (F) of the virtual images formed in the mirror and the center of curvature (2F) are two imaginary points in the mirror that cannot be reached. This results in the formation of images that can’t be projected onto a screen as the image will be inside the mirror. So, from a distance, the image of the object will appear smaller but it will get larger as the object gets closer to the mirror.
- In the above diagram, the center of the original sphere is called the center of curvature while the principal axis is the line that passes from the surface of the mirror through the center of the sphere.
- F is the focal point of the mirror and is located along the principal axis midway between the center of curvature and the surface of the mirror.
- Both the focal point and the center of curvature are located opposite the object on the side of the mirror.
- Since the focal point is always behind the convex mirror the focal length will always be negative.
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Image Formation by Convex Mirror
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There are two possibilities of image formation depending on the position of the object in a convex mirror
- When the object is at infinity and
- When the object is between infinity and the pole.
When the Object is at Infinity
When an object is placed at the infinity of a convex mirror, a point-sized image is formed behind the mirror at the principal focus. The image thus formed will be highly diminished, virtual and erect.
When the Object is placed between Infinity and Pole
When the object is placed between the infinity and pole of a convex mirror, the image formed will be diminished, virtual and erect, and will be formed in between the pole and the focus, that is, behind the mirror.
When the Object is placed between Infinity and Pole
Uses of Convex Mirror
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Convex Mirrors have a number of applications in day-to-day life. Here are some of the important functions of a concave mirror.
Convex Mirror In Automobiles
Automobiles have rearview and side-view mirrors that help the drivers with the same. Convex mirrors are used as rearview mirrors in automobiles to help the drivers get a good view of the road and the vehicles behind them. Convex mirror in automobiles helps the drivers foresee risky situations and thus avoid accidents.
Convex Mirrors in Automobiles
- Convex mirrors have broader fields of view when compared to concave and plane mirrors.
- The concave mirrors are capable of providing a fish-eye view to the person who is driving an automobile and this feature helps them get a clear rear view of the roads and the different vehicles around them.
- The virtual image that is formed by the mirror will also be smaller than the actual size thus providing a wider field view for the driver.
Convex Mirror in Mobile Cameras
Mobile cameras that have selfie cameras built into them use a convex mirror to capture self-portrait shots.
Convex Mirrors in ATM [Automated Teller Machines]
Convex mirrors are placed close to ATM or automated teller machines so as to allow the customers to see if there is anyone standing behind them. This helps in ensuring the security of the customers while they are using the ATM. It helps in avoiding the issue of theft of the withdrawal money and also keeps the identity of the ATM user safe.
Convex Mirrors in ATMs
Convex Mirrors in Street Lights
Convex mirrors are used in streetlights as they have the ability to spread light rays over a wider area.
Convex Mirrors in In Street Lights
In Sunglasses
Convex Mirrors are used for developing a sunglass lens. The purpose of using convex mirrors in a sunglass is to reflect the sunlight away from the person that is wearing it.
In Production Processes
Convex Mirrors have an important role to play in the work environment. These mirrors are attached to conveyor belts to view products from different angles. This helps in enhancing the quality of the product as this will help avoid any faults that may get caused at the time of production.
In Magnifying glasses
Magnifying glasses are actually formed by placing two convex mirrors together.
Convex Mirrors in Magnifying Glasses
In Telescope
Telescopes are made using convex mirrors so as to view farther objects clearly as point-sized images.
Convex Mirrors in Telescope
Difference Between Concave and Convex Mirror
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The main differences between concave and convex mirrors are –
- A convex mirror is also called a fish-eye mirror or diverging mirror since the reflecting side of these mirrors bulges outwards in the direction of the light source. However, in the case of a concave mirror, the reflecting side bugles inwards.
- The images formed by convex mirrors are highly diminished. However, concave mirrors form magnified images of the objects.
- Concave mirrors are thus used in places where it is required to have a magnified image of an object.
Things to Remember on Convex Mirrors
- A convex mirror reflects the light outwards which is why it is not used to focus light.
- Convex or curved mirrors always tend to form a virtual image as the focus and center of curvature are imaginary points inside the mirrors and can not be reached.
- They are generally used as rear and side-view mirrors in cars and as security mirrors in public.
- Convex mirrors give us a wider view than flat or concave mirrors.
- There are two possibilities of image formation depending on the position of the object in a convex mirror; when the object is at infinity and when the object is between infinity and the pole.
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Previous Year Questions
- If in the following figure, height of object is… [DUET 2007]
- A lens of large focal length and large aperture is best suited as an objective… [NEET 2021]
- A concave lens of glass, refractive index 1.5 has both surfaces of same… [JEE Advanced 1999]
- Two plano-concave lenses (1 and 2) of glass of refractive index 1.5 have… [BITSAT 2017]
- A convex lens of glass is immersed in water compared to its power in air… [CBSE CLASS XII]
- A container is filled with water (μ = 1.33) up to a height of 33.25 cm… [JEE Advanced 2005]
- A student performed the experiment of determination of focal length of a… [KEAM 2009]
- The focal length of a spherical mirror made of steel is… [AP EAPCET]
- A spherical surface of radius of curvature R, separates air… [NEET 1998]
- A concave mirror is placed on a horizontal table with its axis directed… [JEE Advanced 1998]
- A convex lens ′A′ of focal length 20cm and a concave lens… [JIPMER 2021]
- Two thin biconvex lenses have focal lengths… [KCET 2021]
- A thin convex lens is made of two materials with refractive indices… [JEE Advanced 2019]
- Colour of light having maximum speed in air is… [KCET 1977]
- A ray parallel to principal axis is incident at… [BITSAT 2015]
Sample Questions on Convex Mirrors
Ques. What is the reason why a convex mirror is called a diverging mirror? (2 marks)
Ans. The convex mirror behaves in a way that it makes light rays diverge after reflecting and hence the convex mirrors are called the diverging mirror. By diverging, it meant that when a light ray is directed towards the mirror the original parallel ray of light diverges/deviates after hitting the reflective surface of the convex mirror.
Ques. How can one recognize a Convex Mirror? (4 marks)
Ans. There are different types of mirrors such as Plane mirrors, Concave mirrors, and convex mirrors and it is fairly easy to distinguish a convex mirror from the other types. The distinguishing can be done by looking at the size of the image.
In a plane mirror, the size of the image formed will be the same as the actual object. In a concave mirror, when the object is placed closer to the mirror the size of the image will get enlarged and one will be able to see an inverted image of the object when it is placed at a far distance from the mirror. Only a concave mirror is capable of generating an inverted image. The image size produced by the concave mirror depends on the placement of the screen. In a convex mirror, however, the image produced will always be small and straight.
Ques. Define the terms: (3 marks)
(i) Pole
(ii) Centre of curvature
(iii) Principal Axis
Ans. (i) Pole: Pole is the center of the reflecting surface of a spherical mirror
(ii) Centre of Curvature: The reflecting surface of a convex mirror or any spherical mirror is part of a sphere. The center of this sphere is called the center of curvature.
(iv)Principal focus: The principal axis is the imaginary line that is passing through the pole and the center of curvature of a convex mirror.
Ques. What are the different applications of a convex mirror? (4 marks)
Ans. The different applications of convex mirrors include
- They are used in the hallways of various institutions like hospitals, colleges, schools, etc.
- They are used as rear and side-view mirrors of automobiles.
- They are used in roads, alleys, and driveways at curves
- They are used in automated teller machines.
Ques. What are the Image Formation possibilities using a convex mirror? (2 marks)
Ans. The possibilities of image formation using a convex mirror depending on the position of the object are:
- At infinity and
- Between the pole and infinity.
Ques. Differentiate between a convex mirror and a concave mirror. (4 marks)
Ans. A convex mirror is also called fish-eye mirrors or diverging mirrors since the reflecting side of these mirrors bulges outwards in the direction of the light source. However, in the case of a concave mirror, the reflecting side bugles inwards.
Another difference between convex and concave mirrors is in the images formed by both. As discussed above, the images formed by convex mirrors are highly diminished. However, concave mirrors form magnified images of the objects. Concave mirrors are thus used in places where it is required to have a magnified image of an object.
Ques. How is an image formed in a convex mirror? (2 marks)
Ans. There are two possibilities of image formation depending on the position of the object in a convex mirror
- When the object is at infinity and
- When the object is between infinity and the pole.
When the Object is at Infinity
When the object is placed at the infinity of a convex mirror, a point-sized image is formed behind the convex mirror at the principal focus. The image thus formed will be highly diminished, virtual and erect.
When the Object is placed between Infinity and Pole
When the object is placed between the infinity and pole of a convex mirror, the image formed will be diminished, virtual and erect, and will be formed in between the pole and the focus, that is, behind the convex mirror.
Ques. Define the focus of a concave mirror. If the radius of a convex mirror is 30 cm, find its focal length. (Foreign 2011)
Ans. Focus is the point on the principal axis where all the rays parallel to it meet after reflection. Since, R = 30 cm and f= R/2 we have, f=+15 cm for a convex mirror.
Ques. An object is placed between infinity and the pole of a convex mirror. Draw a ray diagram and also state the position, the relative size, and the nature of the image formed. (All India 2011) (2 Marks)
Ans. 
Ques. Explain with a diagram why a convex mirror is preferred for rearview mirrors in motor cars? (Foreign 2011) (3 Marks)
Ans. A convex mirror is preferred for rearview mirrors in motor cars as:
(i) It always forms a virtual, erect, and diminished image.
(ii) While using a convex mirror as shown, the field of view increases.
the field of view increases
Ques. Write four properties of an image formed by a convex mirror. (Delhi 2012) (3 Marks)
Ans. Properties of an image formed by a convex mirror:
- The image is always formed behind the mirror, between the pole and its focus.
- It is always virtual and erect.
- The size of the image is always smaller than the object.
- Magnification is always positive.
Ques. The focal length of a convex mirror is 10 cm and the object distance is 20 cm. Determine:
(a) the image distance
(b) the magnification of the image (3 Marks)
Ans. The focal length (f) = -10 cm
The minus sign indicates that the focal point of the convex mirror is virtual
The object distance (do) = 20 cm
The image distance (di) :
1/di = 1/f – 1/do = -1/10 – 1/20 = -2/20 – 1/20 = -3/20
di = -20/3 = -6.7 cm
The minus sign indicates that the image is virtual.
The magnification of image :
m = – di / do = -(-6.7)/20 = 6.7/20 = 0.3 (m = 0,3 times smaller than the object.)
Ques. A 10-cm high object is placed in front of a convex mirror with focal length 20 cm.
Determine the image height if the object distance is (a) 10 cm (b) 30 cm (c) 40 cm (d) 50 cm (5 Marks)
Ans. The focal length of convex mirror (f) = -20 cm
The minus sign indicates that the focal point is virtual
The radius of curvature (r) = 2 f = 2(20) = 40 cm
The object height (h) = 10 cm
a) the focal length (f) = -20 cm and the object distance (do) = 10 cm
The image distance (di) :
1/di = 1/f – 1/do = -1/20 – 1/10 = -1/20 – 2/20 = -3/20
di = -20/3 = -6.7
The minus sign indicates that the image is virtual or the image is behind the mirror.
The magnification of image (m) :
m = –di / do = -(-6.7)/10 = 6.7/10 = 0.67
The image height (hi) :
m = hi / ho
hi = ho m = (10 cm)(0.67) = 6.7 cm
b) the focal length (f) = -20 cm and the object distance (do) = 30 cm
The image distance (di) :
1/di = 1/f – 1/do = -1/20 – 1/30 = -3/60 – 2/60 = -5/60
di = -60/5 = -12
The magnification of image (m) :
m = –di / do = -(-12)/30 = 12/30 = 0.4
The height of image (hi) :
m = hi / ho
hi = ho m = (10 cm)(0.4) = 4 cm
c) The focal length (f) = -20 cm and the object distance (do) = 40 cm
1/di = 1/f – 1/do = -1/20 – 1/40 = -2/40 – 1/40 = -3/40
di = -40/3 = -13.3
The magnification of image (m) :
m = – di / do = -(-13.3)/40 = 13.3/40 = 0.3
The image height (hi) :
m = hi / ho
hi = ho m = (10 cm)(0.3) = 3 cm
d) The focal length (f) = -20 cm and the object distance (do) = 50 cm
The image distance (di) :
1/di = 1/f – 1/do = -1/20 – 1/50 = -5/100 – 2/100 = -7/100
di = -100/7 = -14.3
The magnification of image (m) :
m = – di / do = -(-14.3)/50 = 14.3/50 = 0.3
The image height (hi) :
m = hi / ho
hi = ho m = (10 cm)(0.3) = 3 cm
Ques. A convex mirror has a focal length of -10.8 cm. An object is placed 32.7 cm from the mirror's surface. Determine the image distance. (3 Marks)
Ans. di = -8.1 cm
Using the equation 1 / f = 1 / do + 1 / di where f = -10.8 cm and do = + 32.7 cm
Ques. Determine the focal length of a convex mirror that produces an image that is 16.0 cm behind the mirror when the object is 28.5 cm from the mirror. (3 Marks)
Ans. Using the equation 1 / f = 1 / do + 1 / di where do = 28.5 cm and di = -16.0 cm
(Note: image distances for convex mirrors are always negative.)
Substitute and solve for f.
Answer will be: f = -36.6 cm
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