the magnification caused by a convex lens is represented by Hi/Ho, where hi is the height of the image and ho is the height of the object. Using that ratio, show that the magnification caused by a convex lens is equal to di/do(ratio of the image distance to the object distance.
From similar triangles:
Hi/di =Ho/do
=> Hi/Ho=di/do =M
fairly simple
M=hi/ho
also M=-di/do
therefore
M=hi/ho
-di/do=hi/ho
hi/ho=hi/ho
error:
fairly simple
M=hi/ho
also M=-di/do
therefore
M=hi/ho
-di/do=hi/ho
hi/ho=-di/do
To prove that the magnification caused by a convex lens (M) is equal to the ratio of the image distance (di) to the object distance (do), we can follow these steps:
Step 1: Start with the given equation for magnification:
M = hi / ho
Step 2: Rewrite the equation using similar triangles:
M = hi / ho = di / do
Step 3: Explain why the equation above is valid:
By using similar triangles, we can establish a relationship between the heights and distances of the image and object formed by a convex lens. The height of the image (hi) is proportional to the height of the object (ho) by the same ratio as the distance of the image (di) is to the distance of the object (do). This is because the shape of the lens allows for the triangles formed by the object and image to be similar.
Step 4: Simplify the equation to show that M = di / do:
By cross-multiplying, we get:
hi * do = ho * di
Dividing both sides of the equation by ho * do, we have:
hi / ho = di / do
Therefore, we have proven that the magnification caused by a convex lens (M) is equal to the ratio of the image distance (di) to the object distance (do), which can be represented as M = di / do.