An object is placed at a distance of 60 cm from a converging lens with a focal length of 20cm. What is the magnification of the lens?
(I shall use the Cartesian Sign Convention)
Object distance = u = - 60cm
Focal length = f = + 20cm (The focal length of a converging lens is taken as positive)
Image distance = v
As per the lens formula,
(1/v) = (1/u) + (1/f)
(1/v) = (1/20) - (1/60)
v = 30 cm
Magnification = -(v/u)
= 30/60
= 0.5
Why do object distance consider as negative
Oh dear, I think I need to borrow a magnifying glass to answer this one! But since I don't have one, I'll just have to use my imagination.
Now, let's see. A converging lens... sounds like it knows how to bring things closer together, just like a matchmaker! And we have an object hanging out at a distance of 60 cm, minding its own business.
Since we're talking about magnification, it means we need to find out how much bigger or smaller the image is compared to the object. So let's put on our detective hats and start investigating!
The formula for magnification (m) is given as the ratio of the image distance (di) to the object distance (do). And remember, dear friend, a converging lens has a positive focal length.
So, plugging in the values we know, we get:
m = -di / do
But fear not, my friend! I'm here to make things fun and simple. Now, here's a magical twist to the formula: If the image is real and on the same side as the object (which it is in our case), then the magnification is positive! Hooray for positive vibes!
So, let's find the image distance (di) first. We can use the lens formula:
1/f = 1/do + 1/di
Plugging in the values, we find:
1/20 = 1/60 + 1/di
Now let's solve for di:
1/di = 1/20 - 1/60 = 3/60 - 1/60 = 2/60 = 1/30
Inverting both sides, we get:
di = 30 cm
Now that we have the image distance, we can find the magnification (m):
m = -di / do = -30 / 60 = -0.5
So, the magnification of the converging lens is -0.5. But remember, dear friend, the negative sign just tells us that the image is inverted.
I hope that brought a smile to your face, even if the image is a bit topsy-turvy!
To find the magnification of a lens, we can use the formula:
Magnification (m) = - (image distance / object distance)
Given information:
Object distance (u) = 60 cm
Focal length (f) = 20 cm
Since the lens is converging, the focal length is positive.
First, we need to find the image distance (v). We can use the lens formula:
1/f = 1/v - 1/u
Rearranging the formula to solve for v:
1/v = 1/f - 1/u
1/v = 1/20 - 1/60
1/v = (3 - 1) / 60
1/v = 2/60
1/v = 1/30
v = 30 cm
Now we can calculate the magnification using the formula:
m = - (v / u)
m = - (30 / 60)
m = -0.5
Therefore, the magnification of the lens is -0.5.
To find the magnification of a lens, you can use the formula:
Magnification (m) = - (image distance / object distance)
Given:
Object Distance (u) = 60 cm
Focal Length (f) = 20 cm
First, we need to calculate the image distance. For a converging lens, the image is formed on the opposite side of the object, which means the image distance (v) will be positive.
Using the lens formula:
1/f = 1/v - 1/u
Substituting the values:
1/20 = 1/v - 1/60
To simplify this equation, we can find a common denominator by multiplying both sides by 60v:
3v - v = 60 - 20
Simplifying further:
2v = 40
Dividing both sides by 2:
v = 20 cm
Now that we have the image distance (v) and the object distance (u), we can find the magnification (m):
m = - (v/u)
m = - (20/60)
m = - 1/3
Therefore, the magnification of the lens is -1/3.