A lens forms a real image that is three times the size of the object. If the obj
Practice Questions
Q1
A lens forms a real image that is three times the size of the object. If the object is placed 20 cm from the lens, what is the focal length of the lens?
10 cm
15 cm
5 cm
20 cm
Questions & Step-by-Step Solutions
A lens forms a real image that is three times the size of the object. If the object is placed 20 cm from the lens, what is the focal length of the lens?
Step 1: Understand the problem. We have a lens that creates a real image that is three times larger than the object.
Step 2: Identify the given information. The object distance (u) is 20 cm, and the magnification (m) is 3.
Step 3: Use the magnification formula. The magnification (m) is given by m = -v/u, where v is the image distance.
Step 4: Rearrange the magnification formula to find v. Since m = 3, we have 3 = -v/20.
Step 5: Solve for v. Multiply both sides by -20: v = -60 cm.
Step 6: Use the lens formula. The lens formula is 1/f = 1/v - 1/u.
Step 7: Substitute the values into the lens formula. We have u = -20 cm (object distance is negative in lens formula) and v = -60 cm.
Magnification – The ratio of the height of the image to the height of the object, which can also be expressed in terms of the image distance (v) and object distance (u) as m = -v/u.
Lens Formula – The relationship between the focal length (f), object distance (u), and image distance (v) given by the formula 1/f = 1/v + 1/u.
