video lectute for Mirror Formula
Question 1. An object is placed at a distance of `12 cm` in front of a concave mirror of radius of curvature `30 cm`. List four characteristics of the image formed by the mirror. (Delhi 2017)
Question 2. To construct a ray diagram we use two rays of light which are so chosen that it is easy to determine their directions after reflection from the mirror. Choose these two rays and state the path of these rays after reflection from a concave mirror. Use these two rays to find the nature and position of the image of an object placed at a distance of `15 cm` from a concave mirror of focal length `10 cm`. (Delhi 2015, AI 2012)
Question 3. A spherical mirror produces an image of magnification `-1.0` on a screen placed at a distance of `30 cm` from the pole of the mirror.
(i) Write the type of mirror in this case.
(ii) What is the focal length of the mirror?
(iii) What is the nature of the images formed?
Question 4. A student wants to obtain an erect image of a candle flame using a concave mirror of focal length `15 cm`. What should be the range of distance of the candle flame from the mirror? State the nature and size of the image he is likely to observe. Draw a ray diagram to show the image formation in this case. (Foreign 2014)
Question 5. (a) If the image formed by a mirror for all positions of the object placed in front of it is always diminished, erect and virtual, state the type of the mirror and also draw a ray diagram to justify your answer. Write one use such mirrors are put to and why?
(b) Define the radius of curvature of spherical mirrors. Find the nature and focal length of a spherical mirror whose radius of curvature is `+24 cm`. (AI 2017)
Question 6. Calculate the magnification of the image of an object placed perpendicular to the principal axis of a concave mirror of focal length `15 cm`. The object is at a distance of `20 cm` from the mirror. (Delhi 2013)
Question 7. (a) A concave mirror of focal length `10 cm` can produce a magnified real as well as virtual image of an object placed in front of it. Draw ray diagrams to justify this statement,
(b) An object is placed perpendicular to the principal axis of a convex mirror of focal length `10 cm`. The distance of the object from the pole of the mirror is `10 cm`. Find the position of the image formed. (2020)
Question 8. (a) If the image formed by a mirror for all positions of the object placed in front of it is always diminished, erect and virtual, state the type of the mirror and also draw a ray diagram to justify your answer. Write one use such mirrors are put to and why? (b) Define the radius of curvature of spherical mirrors. Find the nature and focal length of a spherical mirror whose radius of curvature is `+24 cm`. (AI2017)
Question 9. A student has focused the image of a candle flame on a white screen using a concave mirror. The situation is given below:
Length of the flame `= 1.5 cm`
Focal length of the mirror `= 12 cm`
Distance of flame from the mirror `= 18 cm`
If the flame is perpendicular to the principal axis of the mirror, then calculate the following:
(a) Distance of the image from the mirror
(b) Length of the image
If the distance between the mirror and the flame is reduced to `10 cm`, then what would be observed on the screen? Draw a ray diagram to justify your answer from this situation. (Foreign 2015)
Question 10. List the sign conventions for reflection of light by spherical mirrors. Draw a diagram and apply these conventions in the determination of focal length of a spherical mirror which forms a three times magnified real image of an object placed 16 cm infront of it. (Delhi 2012)
Answer Key
Q1: Answer:
Radius of curvature `(R) = 30 cm`, object distance is `12 cm` in front of the mirror. Thus we can say that object is placed between focus and pole. Four characteristics of the image formed by die given concave mirror when object is placed between pole and focus are:
(i) Virtual
(ii) Erect
(iii) Enlarged
(iv) Image is formed behind the mirror
Q2: Answer:
We use two rays of light, one passing through the centre of curvature of a concave mirror, and another is parallel to the principal axis. After reflection, the ray passing through the centre of a concave mirror is reflected back along the same path and the ray parallel to the principal axis will pass through the principal focus.
`u = -15 cm, f= -10 cm`
From ray diagram, `v = -30 cm`, i.e., beyond `C` Nature of image is real, inverted and magnified.
Q3: Answer:
(i) The mirror is concave mirror.
(ii) Distance the image from the mirror `= – 30 cm`
Magnification, `m=-\frac{v}{u}`
Here `m = – 1` and `v = – 30 cm`
`-1=\frac{-(-30)}{u}`
`∴ u = – 30 cm`
As `v = u`, object is placed at centre of curvature. Therefore, focal length of the mirror,
`f = \frac{−30}{2} = – 15 cm`
(iii) Image formed is real and inverted and of the same size of the object.
Q4: Answer:
To obtain an erect image of an object, the object should be placed in between pole and focus. Range of distance of the candle flame from the mirror is in between `15 cm`.
Nature of the image = Virtual and erect
Size of the image = Enlarged
For ray diagram, refer to answer `40`.
Q5: Answer:
(a) If the image formed by a mirror for all positions of the object placed in front of it is always diminished, erect and virtual then the mirror is convex mirror.
The ray diagrams for the formation of image by a convex mirror for the first position when the object is at infinity and the second position when the object is at a finite distance from the mirror are shown.
Use of Convex Mirrors
Convex mirrors are commonly used as rear-view (wing) mirrors in vehicles because they always give an erect, though diminished image. Also, they have a wider field of view as they are curved outwards. Thus, convex mirrors enable the driver to view a large area.
(b) Radius of Curvature: The radius of the sphere of which the reflecting surface of a spherical mirror forms a part, is called the radius of curvature of the mirror. It is represented by the letter `R`.
∵ The radius of curvature is equal to twice the focal length.
`∴ R = 2f`
If `R=+24cm, f=R/2=24/2=12cm`
Since the radius of curvature is positive, the mirror is convex mirror. Hence the nature of the image is virtual and erect.
Q6: Answer:
Given, focal length of concave mirror,
`f = -15 cm`
Object distance, `u = -20 cm`
Image distance, `v = ?`
Using mirror formula,
Using magnification formula,
`m=-\frac{v}{u}=-\frac{-60}{-20} or `m=-3`
So, the magnification,`m = -3`.
Q7: Answer:
(a) A magnified real image is produced in a concave mirror when the object is placed between principal focus and centre of curvature.
A magnified virtual image is produced in a concave mirror when the object is placed between the pole and the principle focus of the mirror.
(b) Given, `f = +10 cm` (convex mirror) and `u = -10 cm`
From mirror formula,
Q8: Answer:
(a) If the image formed by a mirror for all positions of the object placed in front of it is always diminished, erect and virtual then the mirror is convex mirror.
The ray diagrams for the formation of image by a convex mirror for the first position when the object is at infinity and the second position when the object is at a finite distance from the mirror are shown.
Use of Convex Mirrors
Convex mirrors are commonly used as rear-view (wing) mirrors in vehicles because they always give an erect, though diminished image. Also, they have a wider field of view as they are curved outwards. Thus, convex mirrors enable the driver to view a large area.
(b) Radius of Curvature: The radius of the sphere of which the reflecting surface of a spherical mirror forms a part, is called the radius of curvature of the mirror. It is represented by the letter R.
∵ The radius of curvature is equal to twice the focal length.
`∴ R = 2f`
If `R=+24cm \Rightarrow f=\frac{R}{2}=\frac{24}{2}=12cm`
Since the radius of curvature is positive, the mirror is convex mirror. Hence the nature of the image is virtual and erect.
Q9: Answer:Given: focal length of the concave mirror, `f = – 12 cm` Length of the flame, `h = 1.5 cm` Distance of flame from the mirror, `u = -18 cm`
(b) Let `h’` be the length of the image.
∵ Magnification, `m=\frac{h'}{h}=-\frac{v}{u}`
`∴ h'=\frac{-vh}{u}=\frac{-(-36)\times1.5}{-18}=-3cm`
If the distance between the mirror and the flame is reduced to `10 cm`, then
`\frac{1}{v}=\frac{1}{f}-\frac{1}{u}=\frac{1}{-12}-\frac{1}{-10}=\frac{1}{60}`
`∴ v = 60 cm`
Hence, image is formed behind the mirror.
Q10: Answer:
Sign Convention for Reflection by Spherical Mirrors : While dealing with the reflection of light by spherical mirrors, we shall follow a set of sign conventions called the New Cartesian Sign Convention, the conventions are as follows:
(i) The object is always placed to the left of the mirror. This implies that the light from the object falls on the mirror from the left-hand side.
(ii) All distances parallel to the principal axis are measured from the pole of the mirror.
(iii) All the distances measured to the right of the origin (along `+ x-axis`) are taken as positive while those measured to the left of the origin (along `– x-axis`) are taken as negative.
(iv) Distances measured perpendicular to and above the principal axis (along `+y-axis`) are taken as positive.
(v) Distances measured perpendicular to and below the principal axis (along`-y-axis`) are taken as negative.
Given that `m = -3` (real image), `u = -16 cm`
Magnification, `m = -\frac{v}{u}`
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