A concave mirror produces a virtual image of an object placed 10 cm in front of
Practice Questions
Q1
A concave mirror produces a virtual image of an object placed 10 cm in front of it. If the focal length of the mirror is 5 cm, what is the distance of the image from the mirror?
5 cm
10 cm
15 cm
20 cm
Questions & Step-by-Step Solutions
A concave mirror produces a virtual image of an object placed 10 cm in front of it. If the focal length of the mirror is 5 cm, what is the distance of the image from the mirror?
Step 1: Identify the given values. The focal length (f) of the concave mirror is 5 cm, but since it's a concave mirror, we use -5 cm. The object distance (u) is 10 cm in front of the mirror, so we use -10 cm.
Step 2: Write down the mirror formula: 1/f = 1/v + 1/u.
Step 3: Substitute the values into the formula: 1/(-5) = 1/v + 1/(-10).
Step 4: Simplify the equation: -1/5 = 1/v - 1/10.
Step 5: To combine the fractions, find a common denominator. The common denominator for 5 and 10 is 10.
Step 7: Add 1/10 to both sides: -2/10 + 1/10 = 1/v.
Step 8: Simplify the left side: -1/10 = 1/v.
Step 9: Take the reciprocal of both sides to find v: v = -10 cm.
Step 10: Interpret the result: The negative sign indicates that the image is virtual and located 10 cm behind the mirror.
Mirror Formula – The relationship between the focal length (f), object distance (u), and image distance (v) in mirror optics, given by 1/f = 1/v + 1/u.
Sign Convention – Understanding the sign conventions for distances in optics, where distances measured in the direction of the incoming light are negative.
Virtual Images – Characteristics of virtual images produced by concave mirrors, which are formed on the same side as the object and cannot be projected onto a screen.
