i have a question on thin lens equation
how do i know when di is positive or negative?
also i have an example:
A convex lens has a focal length of 60 cm. A candle is placed 50 cm from the lens. What type of image is formed and how far is the image from the lens?
(Is my answer correct?)
G f=60cm
do=50cm
R di=?
A 1/f=1/do+1/di
1/di=1/f-1/do
S 1/di=1/60-1/50
1/di=-1/300
di=-300
P Therefore, the image is virtual and it is -300 cm away from the lens.
To determine whether di (the distance of the image from the lens) is positive or negative, you need to consider the sign conventions used in the thin lens equation.
In the thin lens equation, the sign convention can be as follows:
- The focal length (f) is positive for a converging lens (convex) and negative for a diverging lens (concave).
- The object distance (do) is positive if the object is on the same side as the incident light, and negative if the object is on the opposite side.
- The image distance (di) is positive if the image is on the opposite side as the incident light (real image), and negative if the image is on the same side as the incident light (virtual image).
Now, let's apply this to your example:
Given:
f = 60 cm (positive, as it is a convex lens)
do = 50 cm (positive, as the object is on the same side as the incident light)
Using the thin lens equation:
1/f = 1/do + 1/di
1/di = 1/f - 1/do
1/di = 1/60 - 1/50
1/di = -1/300
di = -300 cm
Therefore, the image formed by the convex lens is virtual, and the image distance (di) is -300 cm.
To determine whether di is positive or negative in the thin lens equation, you need to consider the sign conventions used in optics.
In the sign convention for lens equations:
- The distances measured from the lens towards the object are considered positive.
- The distances measured from the lens towards the image are considered negative.
So, in the thin lens equation, if the value of di is positive, it means the image is formed on the opposite side of the lens from the object. If the value of di is negative, it means the image is formed on the same side as the object.
Now, let's analyze your example:
Given:
focal length (f) = 60 cm
object distance (do) = 50 cm
Using the thin lens equation:
1/f = 1/do + 1/di
Substituting the given values:
1/60 = 1/50 + 1/di
To solve for di, subtract 1/50 from both sides of the equation:
1/di = 1/60 - 1/50
Simplifying this equation by finding the common denominator:
1/di = (5 - 6)/300
1/di = -1/300
Now, to determine the type of image and its distance from the lens, we can see that di is negative (-1/300). This indicates that the image is formed on the same side as the object.
Therefore, your answer is correct. The image formed by the convex lens is virtual, and its distance from the lens is -300 cm (which means it is 300 cm on the same side as the object).