Q. 35

List the new Cartesian sign convention for reflection of light by spherical mirrors. Draw a diagram and apply these conventions for calculating the focal length and nature of a spherical mirror which forms 1/3 times magnified virtual image of an object placed 18 cm if front of it.

Answer :

According to the new Cartesian system the Pole (P) of the mirror is taken as the origin and the Principal axis is taken as the horizontal X- axis. The sign conventions for it are as follows:

The object is always placed on the left side of the mirror.


All the distances measured to the right side of the origin are taken as positive, while the distances measured to the left side of the origin are taken as negative.


All the distances parallel to the principal axis of the mirror are measured from the pole of the mirror.


Distances measured vertically upwards from the principal axis of the mirror are taken as positive.


Distances measured vertically downwards from the principal axis of the mirror are taken as negative.


The focal length of Concave mirror is negative while that of convex mirror is positive.


The figure below illustrates the conventions used.



Given;


Magnification (m) (virtual image is always erect).


Object distance (u) = -18cm.


By Magnification Formula;


Magnification,


Where,


v is the image distance


u is the object distance




v= 6cm.


Image distance (v) = 6cm.


By mirror formula;







Therefore, the focal length is 9 cm. Since the focal length is positive, therefore the mirror is convex mirror.


Figure below shows the ray diagram for the same.



Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Foundation | NTSE Most Challenging NumericalsFoundation | NTSE Most Challenging NumericalsFoundation | NTSE Most Challenging Numericals37 mins
Introduction to Spherical LensIntroduction to Spherical LensIntroduction to Spherical Lens42 mins
NCERT | Light- Reflection and Refraction (Part -1)NCERT | Light- Reflection and Refraction (Part -1)NCERT | Light- Reflection and Refraction (Part -1)37 mins
Foundation | How to Solve Numericals on Mirror FormulaFoundation | How to Solve Numericals on Mirror FormulaFoundation | How to Solve Numericals on Mirror Formula58 mins
NCERT | Power of a LensNCERT | Power of a LensNCERT | Power of a Lens31 mins
MTG | Part - 1 (Reflection and Refrection)MTG | Part - 1 (Reflection and Refrection)MTG | Part - 1 (Reflection and Refrection)50 mins
Foundation | Total Internal ReflectionFoundation | Total Internal ReflectionFoundation | Total Internal Reflection35 mins
Quiz | Introduction to LightQuiz | Introduction to LightQuiz | Introduction to Light55 mins
Rapid Fire Quiz on Reflection and RefractionRapid Fire Quiz on Reflection and RefractionRapid Fire Quiz on Reflection and Refraction49 mins
What is Refraction?What is Refraction?What is Refraction?45 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses