A convex mirror of focal length 30cm. produces a real and inverted image of magnification 0.5.by how much distance the object should be brought closer to obtain a virtual and erect image of magnification 2?
PLS. ANSWER ITS URGENT
To find out how much distance the object should be brought closer to obtain a virtual and erect image of magnification 2, we need to use the mirror formula and the magnification formula.
- The mirror formula is given as: 1/f = 1/v - 1/u
- The magnification formula is given as: m = -v/u
Where:
- f is the focal length of the mirror (in this case, 30 cm)
- v is the image distance
- u is the object distance
- m is the magnification
Given that the real and inverted image has a magnification of 0.5, we can calculate the image distance using the magnification formula.
m = -v/u
0.5 = -v/u
Next, we need to solve the mirror formula for the given situation to find the object distance (u) for the real and inverted image.
1/f = 1/v - 1/u
1/30 = 1/v - 1/u
Let's denote the object distance for the real and inverted image as 'u1' and the image distance as 'v1'. To solve for u1, we need to know the value of v1.
Now, we want to find the new object distance (u2) for a virtual and erect image with a magnification of 2. To solve for u2, we need to use the magnification formula again.
m = -v/u
2 = -v/u2
We can now use the mirror formula for the virtual and erect image to find the image distance (v2) using the values of u2 and f.
1/f = 1/v2 - 1/u2
1/30 = 1/v2 - 1/u2
Finally, we can calculate the difference in distance between the two object positions (u2 - u1) to find out how much closer the object needs to be brought.
(u2 - u1) = u1 - u2
By solving these equations, we can find the required distance.