A diverging lens has a focal length of -10 cm. What is the image distance when t

A diverging lens has a focal length of -10 cm. What is the image distance when the object is placed at 5 cm?

A diverging lens has a focal length of -10 cm. What is the image distance when the object is placed at 5 cm?

Step 1: Identify the given values. The focal length (f) of the diverging lens is -10 cm, and the object distance (u) is 5 cm.
Step 2: Write down the lens formula: 1/f = 1/v - 1/u.
Step 3: Substitute the known values into the lens formula: 1/(-10) = 1/v - 1/5.
Step 4: Simplify the equation: -0.1 = 1/v - 0.2.
Step 5: Rearrange the equation to isolate 1/v: 1/v = -0.1 + 0.2.
Step 6: Calculate the right side: 1/v = 0.1.
Step 7: Take the reciprocal to find v: v = 1/0.1 = 10 cm.
Step 8: Since the lens is diverging, the image distance (v) will be negative, so v = -10 cm.

Lens Formula – The lens formula relates the focal length (f), image distance (v), and object distance (u) of a lens, expressed as 1/f = 1/v - 1/u.
Diverging Lens Characteristics – A diverging lens has a negative focal length and produces virtual images when the object is placed within its focal length.
Sign Convention – Understanding the sign convention for lenses is crucial, where distances measured in the direction of the incoming light are negative.