A concave mirror has a focal length of 20 cm. What is the distance of the object
Practice Questions
Q1
A concave mirror has a focal length of 20 cm. What is the distance of the object from the mirror if the image formed is at a distance of 30 cm from the mirror? (2021)
10 cm
15 cm
25 cm
30 cm
Questions & Step-by-Step Solutions
A concave mirror has a focal length of 20 cm. What is the distance of the object from the mirror if the image formed is at a distance of 30 cm from the mirror? (2021)
Step 1: Identify the given values. The focal length (f) of the concave mirror is 20 cm, so we write f = -20 cm (negative for concave mirrors). The image distance (v) is 30 cm, so we write v = -30 cm (negative because the image is on the same side as the object).
Step 2: Write down the mirror formula: 1/f = 1/v + 1/u, where u is the object distance we want to find.
Step 3: Substitute the known values into the mirror formula: 1/(-20) = 1/(-30) + 1/u.
Step 5: Rewrite the equation: -1/20 = -1/30 + 1/u.
Step 6: To isolate 1/u, add 1/30 to both sides: 1/u = -1/20 + 1/30.
Step 7: Find a common denominator for -1/20 and 1/30, which is 60. Rewrite the fractions: -1/20 = -3/60 and 1/30 = 2/60.
Step 8: Now combine the fractions: 1/u = -3/60 + 2/60 = -1/60.
Step 9: To find u, take the reciprocal: u = -60 cm.
Step 10: Since we are looking for the distance of the object from the mirror, we take the absolute value: u = 60 cm.
Mirror Formula – The relationship between the focal length (f), image distance (v), and object distance (u) for mirrors, expressed as 1/f = 1/v + 1/u.
Sign Convention – Understanding the sign conventions for concave mirrors, where focal length is negative and image distance is also negative for real images.
