If an object of 7 cm height is placed at a distance of 12 cm from a convex lens of focal
length 8 cm, find the position, and height of the image. Draw a Ray diagram to show
formation of image in this case.
Answers
Answer:
Solution :
First of all we find out the position of the image. By the position of image we mean the distance of image from the lens.
Here, Object distance, u=-12 cm (it is to the left of lens)
Image distance, v=? (To be calculated)
Focal length, f=+8 cm (It is a convex lens)
Putting these values in the lens formula:
1v−1u=1f
We get: 1v−1−12=18
or 1v+112=18
or 1v+112=18
1v=18−112
1v=3−224
1v=124
So, Image distance, v=+24 cm
Thus, the image is formed on the right side of the convex lens. Only a real and inverted image is formed on the right side of a convex lens, so the image formed is real and inverted.
Let us calculate the magnification now. We know that for a lens:
Magnification, m=vu
Here, Image distance, v=24 cm
Object distance, u=−12 cm
So, m=24−12
or m=−2
Since the value of magnification is more than 1 (it is 2), so the image is larger than the object or magnified. The minus sign for magnification shows that the image is formed below the principal axis. Hence, the image is real and inverted. Let us calculate the size of the image by using the formula:
m=h2h1
Here, Magnification, m=−2 (Found above)
Height of object, h1=+7 cm (Measured upwards)
Height of image, h2=? (To be calculated)
Now, putting these values in the above formula, we get:
−2=h27
or h2=−2×7
Thus, Height of image, h2=−14cm
Thus, the height or size of hte image is 14 cm. The minus sign shows that this height is in the downward direction, that is the image is formed below the axis. Thus, the image is real and inverted.
Explanation:
Focal length of convex lens, f=8 cm
Object distance, u=−12 cm
Using lens formula
v
1
−
u
1
=
f
1
where v is the image distance.
∴
v
1
−
−12
1
=
8
1
⟹ v=+24 cm
(+ve sign indicates that image is formed behind the lens)
Hence the image formed is real and inverted.