A convex mirror form an image of height 2.4cm, if the radius of covature of the mirror is 40cm.find the height,distance of the object from the front of the mirror
u=30 h=6
Well, well, well... let's put on our clown noses and solve this problem one laughter at a time!
So, we're dealing with a convex mirror with a radius of curvature of 40cm and an image height of 2.4cm. The question also asks us to find the height and distance of the object from the front of the mirror. Let's get those giggles rolling!
First things first, let's bust out a mirror joke:
Why did the mirror go to school?
Because it wanted to learn how to reflect on its life choices!
Now that we've got that out of our systems, let's get back to the problem. In a convex mirror, the image height is always negative (-2.4cm), so we can use the mirror formula:
1/f = 1/v - 1/u
where f is the focal length, v is the image distance, and u is the object distance. We already know the image height (h) and the focal length (f = R/2), so let's plug in those values and get cracking again!
Now, for another jocular interlude:
Why was the math book sad?
Because it had too many problems!
Okay, back to the task at hand. We can find the height of the object (H) using the magnification formula:
h/v = H/u
where H is the object height. Since we know h = -2.4cm and H is what we're looking for, we can rearrange the formula and solve for H.
But first, let's squeeze in one more clown pun, just for fun:
Why don't scientists trust atoms?
Because they make up everything!
Alright, let's wrap this up. Plug in the given values, solve for H, and chuckle your way to the answer. Remember, laughter is always the best solution!
I hope that helps, and as always, feel free to ask if you have any more questions (or if you just want to hear more clown jokes!).
To solve this problem, we can use the mirror formula for convex mirrors:
1/f = 1/v - 1/u
Where:
f = focal length of the mirror
v = image distance
u = object distance
Since the mirror is convex, the focal length is positive, given by f = R/2, where R is the radius of curvature.
Given:
Radius of curvature (R) = 40 cm
Image height (h') = 2.4 cm
Step 1: Find the focal length (f)
We know that f = R/2
f = 40 cm / 2 = 20 cm
Step 2: Find the object distance (u)
Using the mirror formula: 1/f = 1/v - 1/u
Since the object distance (u) is given, we can rearrange the formula to solve for the image distance (v).
1/v = 1/f + 1/u
1/v = 1/20 + 1/u
Step 3: Find the height (h) and distance of the object from the front of the mirror
To find the height (h) and distance of the object from the front of the mirror, we can use the magnification formula:
Magnification (m) = -v/u = h'/h
Given that the image height (h') is 2.4 cm, we can solve for the object height (h) using the magnification formula.
m = -v/u
m = -2.4/h
Since the object distance (u) is given, we can rearrange the formula to solve for the height (h).
h = -2.4/m
To find the distance of the object from the front of the mirror, we can use the formula:
Distance from mirror = object distance (u) - object height (h)
Substituting the variables into the formulas:
Using 1/v = 1/20 + 1/u:
1/v = 1/20 + 1/u
1/v = (u + 20)/(20u)
Using m = -v/u:
m = -v/u
-2.4/h = -v/u
Using h = -2.4/m:
h = -2.4/m
Using Distance from mirror = u - h:
Distance from mirror = u - h
By substituting the given values and solving the equations, you will find the height (h) and distance of the object from the front of the mirror.
To find the height and distance of the object from the convex mirror, we can use the mirror formula, which relates the object distance (u), image distance (v), and the focal length (f) of the mirror:
1/f = 1/v + 1/u
Given information:
Radius of curvature (R) = 40 cm
Height of the image (h') = 2.4 cm
Since it is a convex mirror, the focal length will be half the radius of curvature:
f = R/2 = 40/2 = 20 cm
Now, let's find the image distance (v):
1/f = 1/v + 1/u
Since the object is at infinity for a convex mirror, the object distance (u) is considered infinite. Therefore, 1/u becomes 0:
1/f = 1/v + 1/∞
Since 1/∞ is 0, we are left with:
1/f = 1/v
Applying the values:
1/20 = 1/v
Rearranging the equation to solve for v:
v = f = 20 cm
Now that we have the image distance, we can use the mirror magnification formula to find the height of the object (h):
h'/h = -v/u
Given that the height of the image (h') is 2.4 cm and the image distance (v) is 20 cm, we can rearrange the equation to solve for h:
h = -(h' * u) / v
Substituting the values:
h = -(2.4 * u) / 20
We still need the value of the object distance (u) in order to find the height. Unfortunately, the problem statement does not provide the object distance. If you have the object distance, we can substitute that value into the equation and solve for the height.