determine the image distance for an object that is 45.0 cm from a double convex lens having a focal length of 15.0 cm
Let the image distance be Di
1/45 + 1/Di = 1/15
1/Di = 2/45
Di = 22.5 cm
You do not need to know that the lens is double convex. All you need is the focal length.
To determine the image distance for an object that is 45.0 cm from a double convex lens with a focal length of 15.0 cm, we can use the lens formula:
1/f = 1/v - 1/u
where:
f = focal length of the lens
v = image distance from the lens
u = object distance from the lens
Given:
f = 15.0 cm
u = 45.0 cm
Substituting the values into the lens formula, we have:
1/15.0 = 1/v - 1/45.0
To solve for v, let's find a common denominator:
1/15.0 = (45 - v)/45v
Now, cross-multiply:
45v = 15.0 * (45 - v)
Simplifying:
45v = 675.0 - 15v
Combine like terms:
45v + 15v = 675.0
60v = 675.0
Divide both sides by 60:
v = 11.25 cm
Therefore, the image distance for an object that is 45.0 cm from a double convex lens with a focal length of 15.0 cm is 11.25 cm.
To determine the image distance for an object placed 45.0 cm from a double convex lens with a focal length of 15.0 cm, 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, and
- u is the object distance.
Given values:
f = 15.0 cm (focal length)
u = 45.0 cm (object distance)
Let's substitute these values into the lens formula:
1/15.0 = 1/v - 1/45.0
To simplify the equation, we need to find a common denominator. In this case, it would be 45v:
3/45 = (45 - v)/45v
Cross-multiplying, we have:
3 * 45v = 45 * (45 - v)
135v = 2025 - 45v
Combining like terms:
135v + 45v = 2025
180v = 2025
Dividing both sides by 180:
v = 2025/180
v ≈ 11.25 cm
Therefore, the image distance for an object placed 45.0 cm from a double convex lens having a focal length of 15.0 cm is approximately 11.25 cm.