If a concave lens has a focal length of -10 cm, what is the nature of the image formed when an object is placed at 5 cm from the lens?
Correct Answer: Virtual and upright image
- Step 1: Identify the type of lens. A concave lens is a lens that curves inward.
- Step 2: Note the focal length of the lens. The focal length is given as -10 cm, which indicates it is a concave lens.
- Step 3: Determine the position of the object. The object is placed at 5 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. Here, f = -10 cm and u = -5 cm (object distance is taken as negative in lens formula).
- Step 6: Rearrange the formula to find v: 1/v = 1/f + 1/u.
- Step 7: Calculate 1/v = 1/(-10) + 1/(-5).
- Step 8: Simplify the equation: 1/v = -0.1 - 0.2 = -0.3.
- Step 9: Find v by taking the reciprocal: v = -1/0.3 = -3.33 cm.
- Step 10: Interpret the result. The negative value of v indicates that the image is virtual and located on the same side as the object.
- Step 11: Conclude that concave lenses always produce virtual and upright images.
- Lens Types – Understanding the characteristics of concave lenses, including their focal length and image formation.
- Image Characteristics – Identifying the nature of images (real vs. virtual, upright vs. inverted) produced by different types of lenses.
- Lens Formula – Application of the lens formula (1/f = 1/v - 1/u) to determine image characteristics based on object distance and focal length.
