An object 7.5cm light is placed 30 cm from aconcave mirror of curvature 20cm calculate the 1image distance 2image height
5.26
Well, well, well, let's have some fun with mirrors, shall we?
1. The image distance can be determined using the mirror formula:
1/f = 1/v - 1/u
Where:
f = focal length of the mirror
v = image distance
u = object distance
Now, we know that the curvature (C) of the mirror is equal to twice the focal length (f):
C = 2f
Therefore, f = C/2 = 20/2 = 10 cm
Plugging in the values:
1/10 = 1/v - 1/30
Let's do some math (brace yourself!):
v/300 = 30/30 - 10/30
v/300 = 20/30
v/300 = 2/3
Now, cross-multiply (it sounds dangerous, but it's just math):
v x 3 = 2 x 300
v = 600/3
v = 200 cm
Ta-da! The image distance is 200 cm.
2. Now, for the image height. Let's hope it's not too tall!
The magnification (M) can be calculated using the formula:
M = -v/u
Plugging in the values:
M = -200/30
M = -20/3
The negative sign indicates an inverted image. That's a real head-turner!
The image height (h') can be determined using:
h' = M x h
Since we don't have the actual height of the object (h), we'll have to leave this one unanswered. But hey, at least we solved the image distance!
Keep smiling and have fun with your reflective adventures!
To calculate the image distance and image height using a concave mirror, we can use the mirror formula and magnification formula respectively. Here are the step-by-step calculations:
1. Image Distance:
The mirror formula is given by:
1/f = 1/v - 1/u
Where:
f = focal length of the mirror
v = image distance
u = object distance
Given:
Object distance (u) = 30 cm
Curvature of the mirror (R) = -20 cm (-ve sign indicates concave mirror)
The focal length (f) can be calculated using the formula:
f = R/2
Substituting the values:
f = -20 cm / 2
f = -10 cm
Now, we can substitute the values of f and u in the mirror formula to calculate v:
1/(-10) = 1/v - 1/30
Solving this equation will give us the value of v.
2. Image Height:
The magnification formula is given by:
magnification (m) = -v/u
Given the magnification formula is negative because it is a concave mirror.
We can substitute the values of v and u to calculate the magnification (m). The magnification will give us the image height.
So, now we will calculate the image distance and image height using the given values and formulas.
To calculate the image distance and image height formed by a concave mirror, we can use the mirror formula and magnification formula.
1. Image Distance (v):
The mirror formula is given by:
1/f = 1/u + 1/v
Where:
f is the focal length of the concave mirror,
u is the object distance,
v is the image distance.
In this case, the object distance (u) is given as 30 cm, and the curvature of the mirror (R) is given as 20 cm. The focal length (f) can be calculated using the formula: f = R/2.
Since the object is placed outside the focal point, the object distance (u) will be positive. Plugging in the values, we have:
1/f = 1/u + 1/v
1/(R/2) = 1/30 + 1/v
2/R = 1/30 + 1/v
2/20 = 1/30 + 1/v
1/10 = 1/30 + 1/v
1/10 - 1/30 = 1/v
(3 - 1)/30 = 1/v
2/30 = 1/v
1/15 = 1/v
v = 15 cm
Therefore, the image distance (v) is 15 cm.
2. Image Height (h'):
The magnification formula is given by:
magnification (m) = -v/u = h'/h
Where:
h' is the image height,
h is the object height.
Since no object height is given, we'll assume it to be 1 (unit height).
Plugging in the values, we have:
m = -v/u = h'/h
m = -15/30 = h'/1
m = -1/2 = h'
Therefore, the image height (h') is -1/2.
Note: The negative sign for the magnification (m) indicates that the image is inverted.