Question

A student wants to project the image of a candle flame on a screen 80 cm in front of a mirror by keeping the candle flame at a distance of 20 cm from its pole.
i) Which type of mirror should the student use?
ii) Find the magnification of the image produced.
iii) Find the distance between the object and its image.
iv) Draw a ray diagram to show the image formation in this case and mark the distance between the object and its image.

Answer 1

Hint: At first we find the focal length of the mirror used. Now, if the focal length of the mirror is positive then the mirror is determined as a convex mirror and if the sign is negative then the mirror is determined to be a concave mirror. After that according to the question we need to find the magnification of the image produced with the help of the mirror formula. Now, to find the distance between the object and the image we need to draw the ray diagram by looking at the diagram we can determine the distance between the object and its image.

Formula used:
$\dfrac{1}{f}=\dfrac{1}{v}+\dfrac{1}{u}$
m = - v / u.

Complete step-by-step answer:
According, to the question,
V = - 80cm
U = - 20cm
We know, that mirror formula is,
$\dfrac{1}{f}=\dfrac{1}{v}+\dfrac{1}{u}$ ,
So,
$\dfrac{1}{f}=\dfrac{1}{-80}+\dfrac{1}{-20}$, we know the value of v and u, so we replaced that with the equation.
$f=\dfrac{\left( -80 \right)\times \left( -20 \right)}{\left( -80 \right)+\left( -20 \right)}$,
On solving the above equation we get,
f = - 16 cm
i) So as the focal length of the mirror is negative, the mirror that the student should use to project the image of a candle flame on a screen is a concave mirror.

ii) We know that the formula for magnification is,
m = - v / u.
So,
m = - ( - 80 ) / (-20).
m = -4.
So the magnification of the image produced is -4.
iii)

We can say that, we can get the distance between the object and image from the ray diagram drawn.
iv)
  

Note: In the mirror formula, $\dfrac{1}{f}=\dfrac{1}{v}+\dfrac{1}{u}$, ‘f’ is the focal length, ‘v’ is the distance from the screen to the mirror, ‘u’ is the distance between the object and the mirror. In the magnification formula ‘v’ and ‘u’ are also the same.