A concave lens has a focal length of -20 cm. What is the nature of the image formed when an object is placed at 30 cm from the lens?

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Q: A concave lens has a focal length of -20 cm. What is the nature of the image formed when an object is placed at 30 cm from the lens?

Solution: For a concave lens, the image formed is virtual and erect when the object is placed at any distance.

Steps: 9

Step 1: Identify the type of lens. In this case, it is a concave lens.
Step 2: Note the focal length of the lens, which is -20 cm (the negative sign indicates it is a concave lens).
Step 3: Determine the object distance. The object is placed at 30 cm from the lens.
Step 4: Use the lens formula: 1/f = 1/v - 1/u, where f is the focal length, v is the image distance, and u is the object distance.
Step 5: Substitute the values into the lens formula: 1/(-20) = 1/v - 1/(-30).
Step 6: Simplify the equation: 1/v = 1/(-20) + 1/30.
Step 7: Find a common denominator and solve for 1/v.
Step 8: Calculate the value of v to find the image distance.
Step 9: Determine the nature of the image based on the value of v. For a concave lens, the image is always virtual and erect regardless of the object distance.