Question

A convex lens of focal length 20 cm forms an image 1/4th
of the size of the object, then the position of the image
from the object is​

Answer 1

Answer:

When an object is placed at a distance of 20 cm from a concave mirror of focal length 1/4 th of the size , then the position of the image is at infinity. The is because when an object is placed at the focus of a concave mirror then the image is formed at infinity.

Answer 2

Answer:

For a convex lens of focal length 20 cm which forms an image 1/4th of the size of the object, then the position of the image from the object is​ -60cm.

Explanation :

According to the question, following is the information given to us :

• The mirror in the question is convex mirror

• We know that, convex mirrors are actually curved mirrors with reflective surfaces that protrude in the direction of the light source and this protruding surface does not in-fact serve as a light focus; rather, it reflects light outward. Also we can say that, as the focal point (F) and the centre of curvature (2F) are fictitious positions in the mirror that cannot actually be reached, these mirrors create a virtual image. Furthermore, as a result, images are in reality created that can only be seen in the mirror and cannot be projected onto a screen. So when viewed from a distance, the image appears smaller than the thing, but as the object approaches the mirror, the picture grows

h’ = (1/4)h

f = 20 (positive in this case because of convex mirror)

To find :

Position of the image from the object ?

Solution :

Also, we know that according to magnification formula :  

m = -v/u

• The ratio of the image's height to the object's height is known as magnification. As a result, the definition of magnification is the ratio of v to u with a minus sign. Note: Only in terms of magnitude, a lens's magnification formula and a mirror's are same.

So the above equation can also be represented as :

m = 1/4 = h’/h = -v/u

Therefore, by simplifying it, we get :

v = -u/4

Now, in the next step we will be using mirror formula :

1/f = 1/v + 1/u

Substituting the value of v that we got before, in the above equation, we get :

1/20 = 1/ (-u/4) + 1/u

By simplifying it furthermore, we get :

1/20 = -3/u

Therefore, u = -60 cm

Therefore, the position of the image from the object is -60 cm according to our above calculations.

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