Where should an object be placed in front of a convex lens of focal length 0.12 m to obtain a real image of size three times the size of the object, on the screen?
Answer (2)
Use the magnification formula m = − u v to find the relationship between image distance v and object distance u : v = 3 u .
Apply the lens formula f 1 = v 1 + u 1 .
Substitute v = 3 u and f = 0.12 m into the lens formula: 0.12 1 = 3 u 1 + u 1 .
Solve for u to find the object distance: u = 0.16 m. The object should be placed 0.16 m in front of the lens to obtain the desired image. 0.16 m
Explanation
Problem Analysis We are given a convex lens with a focal length f = 0.12 m. We want to find the object distance u such that the real image formed is three times the size of the object. This means the magnification m = − 3 (negative sign because the image is real and inverted).
Magnification Formula The magnification formula is given by m = − u v , where v is the image distance and u is the object distance. Since m = − 3 , we have − 3 = − u v , which simplifies to v = 3 u .
Lens Formula The lens formula is given by f 1 = v 1 + u 1 , where f is the focal length.
Substitution Substituting v = 3 u into the lens formula, we get 0.12 1 = 3 u 1 + u 1 .
Solving for u Simplifying the equation, we have 0.12 1 = 3 u 1 + 3 u 3 = 3 u 4 3 u = 4 × 0.12 u = 3 4 × 0.12 = 3 0.48 = 0.16 Therefore, u = 0.16 m.
Final Answer The object should be placed at a distance of 0.16 m in front of the convex lens to obtain a real image of size three times the size of the object.
Examples
Understanding lenses helps us design optical instruments like cameras and telescopes. For instance, if you're designing a camera with a lens of focal length 0.12 m and you want the image on the sensor to be three times larger than the object you're photographing, you need to place the object 0.16 m away from the lens. This ensures the image is properly magnified and focused.
To create a real image three times the size of the object using a convex lens with a focal length of 0.12 m, place the object 0.16 m in front of the lens. This is determined using the magnification formula and the lens formula. The relationship between image distance and object distance allows us to calculate the required object distance.
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