Mail us Request for Call Back

Chapter 1: Light - Reflection and Refraction

Q&A -Ask Doubts and Get Answers

Q
Light - Reflection and Reflection

Question:

An object 5.0 cm in length is placed at a distance of 20 cm in front of a convex mirror of radius of curvature 30 cm. Find the position of the image, its nature and size.

Answer:

Here, the given mirror convex.

Object Distance (u) = -20 cm

Radius of curvature (R) = +30 cm

Height of object ({h}{o}) = 5 cm

Image Distance (v) = ?

Object distance (u) is taken negative as their distances from the pole of the mirror is measured opposite to the direction of the incident light.

Using the relation between R and f:

R = 2f

We get,

f = frac{R}{2}

f = frac{30}{2}

f = 15 cm

Now, using the mirror formula

frac{1}{f} = frac{1}{v}+frac{1}{u}

frac{1}{15} = frac{1}{v}+frac{1}{(-20)}

frac{1}{15} = frac{1}{v} - frac{1}{20}
frac{1}{15} +frac{1}{20} = frac{1}{v}

frac{1}{v} = frac{4-3}{60}

frac{1}{v} = frac{7}{60}

v=frac{60}{7}= 8.57 cm

The positive sign of v indicates that the image is formed on the other side of the mirror at a distance of 8.57 cm. That is the image formed is virtual.

Now, magnification

m = frac{Heightquad of quad image (h_i)}{ Heightquad of quad object (h_o)} = frac{sizequad of quad image (v)}{sizequad of quad object (u)}

m=frac{h_i}{h_o}= -frac{v}{u}

m= -frac{v}{u}

m= -frac{8.57}{-20} = 0.428

Here, the magnification is positive and less than 1. The positive sign indicates that the image is erect and value less than 1 indicates that the size of the image is smaller than the object.m = frac{h_i}{h_o}
0.428 = frac{h_i}{5}

h_i = 0.428 imes 5 = 2.14 cm

The positive sign of image height h_i indicates that the image is erect.

Therefore, the image is formed at a distance of 0.428 cm on the other side of the mirror. The image formed is 2.14 cm tall and it is virtual, erect and smaller in size.

Related Questions for Study

Quick Buy

LATEST OFFERS & PROMOTIONS

What our students and parents say about us!

Saiyam is using EduSaksham online courses from past one year. He is able to complete his tutorials, worksheets, and assignments on his own. Once he is done with worksheets, he can check his answers and if he has done any mistakes, then he can check the correct answers and explanations. They have been given so well that he is able to understand them himself and rarely he asks us for any clarification. He enjoys using the platform and has learned and improved a lot in Mathematics. I would recommend EduSaksham to all parents who want their kids to learn in a structured way and also enjoy the learning process.

Neeraj (Saiyam's Father)

I would like to thank Edusaksham on behalf of my son Aditya who attended " Math Olympiad crash course for 5 weeks". As per Aditya, this course helped him to understand new topics like Roman numerals and decimal places which were not taught in his school till date and had a better understanding of other topics. I personally thank EduSaksham for all the help and support.

Geeta Bansal (Aditya's Mother)

We had a good experience with EduSaksham. Because sheets are available online, Vedant enjoyed doing more and more sheets without any reminders. I could leave him on his own as he was very much motivated to cover the topics. Practice is very important in maths but it becomes difficult for us to prepare sheets, I am glad we found EduSaksham where in a lot of in a lot of sheets are available for practice and the quality of questions are also good. As it's a venture from IITians we could think of giving it a try and I am glad we tried

Shikha Chowdhary (Vedant's Mother)

I have grown up in a family where my father used to give me practice maths paper every day which I need to finish before I go to play. I think that strong foundation of solving new questions every day helped me to clear my IITJEE exam. But as working women, I always had time challenge to create practice Math papers for my daughter. Thanks to EduSaksham, their questions are so logical and conceptual that I don't feel the guilt of not creating practice questions by myself :). There are plenty of worksheet along with the tutorials for each chapter. It has made parents life easier :) And the best part is my daughter loves doing it. Thank you EduSaksham.

Anupma (Akshainie's mother)

Choose EduSakshamยฎ
Embrace Better Learning

edusaksham-mobile-app
slider-images

Request a Callback