Q. 135.0( 3 Votes )

An object 4 cm in height, is placed at 15 cm in front of a concave mirror of focal length 10 cm. At what distance from the mirror should a screen be placed to obtain a sharp image of the object. Calculate the height of the image.

OR

At what distance form a concave lens of focal length 20cm a 6cm tall object be placed so as to obtain its image at 15cm from the lens? Also calculate the size of the image formed. Draw a ray diagram to justify your answer for the above situation and label it.

Answer :

The data given is:


the object distance is, u = -15 cm,


the focal length is, f = -10 cm,


the height of the object, ho = 4 cm,


we know that the mirror formula is,


, where,


v is the image distance, u is the object distance and f is the focal length of the mirror, here as the mirror is concave so the focal length is negative (-10 cm).


Calculations:


So, after substituting the data we have,





So, we get .


The screen should be placed 30 cm. in front of the concave mirror so as to obtain a sharp image of the object. The magnification can be calculated by the formula,


,


,


,


The height of the image is 8 cm. and negative sign shows that the image is real and inverted.


OR


The data given is:


the image distance is, v = -15 cm,


the focal length is, f = -20 cm,


the height of the object, ho = 6 cm,


we know that the lens formula is,


, where,


v is the image distance, u is the object distance and f is the focal length of the lens, here as the lens is concave so the focal length is negative (-20 cm).


Calculations:


So, after substituting the data we have,





So, we get .


The object should be placed 60 cm. in front of the concave lens so as to obtain image of the object at the given position. The magnification can be calculated by the formula,


,


,


,


The height of the image is 1.5 cm. and the image is virtual and erect.


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