Say i had a focal length of -12cm in a diverging lens and the object is placed 60cm away what would the distance of the image be?
To determine the distance of the image formed by a diverging lens, you can use the lens formula:
1/f = 1/v - 1/u
where:
- f is the focal length of the lens,
- v is the distance of the image from the lens, and
- u is the distance of the object from the lens.
Given that the focal length (f) is -12 cm and the object distance (u) is 60 cm, we can substitute these values into the formula:
1/-12 = 1/v - 1/60
To solve this equation, we can find the reciprocal of both sides:
-1/12 = 1/v - 1/60
Next, we can combine the fractions on the right side:
-1/12 = (60 - v)/60
To isolate the variable v, we can cross-multiply:
-60 = 12(60 - v)
Simplifying the equation gives us:
-60 = 720 - 12v
Rearranging the equation:
-12v = -720 - 60
-12v = -780
Finally, dividing both sides by -12 gives us:
v = 780/12
Calculating the value:
v = 65 cm
Therefore, the distance of the image formed by the diverging lens would be 65 cm.