A 24mm high object is 15cm in front of a +10cm concave lens . 24cm behind the convex lens is a -10cm concave lens . Calculate the size of the final object.
To calculate the size of the final object, we need to consider the image formed by each lens separately.
First, let's determine the image formed by the +10cm concave lens. We can use the lens formula:
1/f = 1/v - 1/u
Where:
- f is the focal length of the lens
- v is the image distance
- u is the object distance
Given that the object distance (u) is 15cm and the focal length (f) of the +10cm concave lens is -10cm (since it is concave), we can substitute the values into the formula:
1/-10 = 1/v - 1/15
Simplifying the equation, we get:
-1/10 = 1/v - 1/15
To solve for v, we need to find a common denominator:
-1/10 = (15 - v)/(15v)
Multiplying both sides by 15v, we obtain:
-1.5v = 10v - 150
Rearranging the equation, we get:
11.5v = 150
v ≈ 13.04 cm
So, the image formed by the +10cm concave lens is located approximately 13.04 cm from the lens.
Next, let's determine the image formed by the -10cm concave lens. We will again use the lens formula, but this time with the focal length of -10cm:
1/f = 1/v - 1/u
Given that the object distance (u) of this lens is 13.04 cm (the image distance obtained from the previous step) and the focal length (f) of the -10cm concave lens is -10cm, we can substitute the values:
1/-10 = 1/v - 1/13.04
Simplifying the equation, we get:
-1/10 = 1/v - 1/13.04
To solve for v, we need to find a common denominator:
-1/10 = (13.04 - v)/(13.04v)
Multiplying both sides by 13.04v, we obtain:
-1.304v = 10v - 130.4
Rearranging the equation, we get:
11.304v = 130.4
v ≈ 11.52 cm
So, the image formed by the -10cm concave lens is located approximately 11.52 cm from the lens.
Now that we have the final image distance (v), we can calculate the size of the final object. We can use the magnification formula:
Magnification (M) = v/u
Where:
- M is the magnification
- v is the image distance
- u is the object distance
In this case, the object distance (u) is 24mm (or 2.4cm). Plugging in the values:
M = 11.52 cm / 2.4 cm
M ≈ 4.80
The magnification factor is approximately 4.80. Therefore, the size of the final object is 4.80 times the size of the original object.