A lens forms a real image that is twice the size of the object. If the object is

A lens forms a real image that is twice the size of the object. If the object is placed 10 cm from the lens, what is the focal length of the lens?

A lens forms a real image that is twice the size of the object. If the object is placed 10 cm from the lens, what is the focal length of the lens?

Step 1: Understand that the lens formula is 1/f = 1/v - 1/u, where f is the focal length, v is the image distance, and u is the object distance.
Step 2: Identify the object distance (u). The object is placed 10 cm from the lens, so u = -10 cm (we use a negative sign for the object distance in lens formulas).
Step 3: Use the magnification formula, which is M = v/u. We know the image is twice the size of the object, so M = 2.
Step 4: Set up the magnification equation: 2 = v / (-10). This means v = -20 cm (the negative sign indicates a real image on the opposite side of the lens).
Step 5: Now, substitute the values of v and u into the lens formula: 1/f = 1/v - 1/u = 1/(-20) - 1/(-10).
Step 6: Calculate 1/f: 1/f = -1/20 + 1/10 = -1/20 + 2/20 = 1/20.
Step 7: Take the reciprocal to find f: f = 20 cm.

Lens Formula – The relationship between the object distance (u), image distance (v), and focal length (f) of a lens, given by 1/f = 1/v - 1/u.
Magnification – The ratio of the height of the image to the height of the object, which is also equal to the negative ratio of the image distance to the object distance (M = -v/u).