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CBSE Class 10 Science 2020 Delhi Set 1

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Question : 29
Total: 30
Draw a ray diagram in each of the following cases to show the formation of image, when the object is placed :
(i) between optical centre and principal focus of a convex lens.
(ii) anywhere in front of a concave lens.
(iii) at 2F of a convex lens.
State the signs and values of magnifications in the above mentioned cases (i) and (ii).
OR
An object 4.0‌cm in size, is placed 25.0‌cm infront of a concave mirror of focal length 15.0‌cm.
(i) At what distance from the mirror should a screen be placed in order to obtain a sharp image?
(ii) Find the size of the image.
(iii) Draw a ray diagram to show the formation of image in this case.
Solution:  
Sign of magnification = Positive
Value of magnification = Greater than 1
Sign of magnification = Positive
Value of magnification = Greater than 1
OR
Given, size of object, Ho=4‌cm
Object distance, u=−25‌cm
Focal length of concave mirror, f=−15‌cm
(i) As per formula,
‌
1
f
‌=‌
1
v
+‌
1
u

⇒‌‌‌
1
−15
‌=‌
1
v
+‌
1
−25

⇒‌‌‌
1
v
‌=‌
1
−15
−‌
1
−25
=‌
1
−15
+‌
1
25

‌=‌
(−25+15)
375
=‌
(−10)
375

‌=‌
1
−37.5

⇒‌‌‌
1
v
‌=‌
1
−37.5

⇒‌‌v‌=−37.5‌cm
∴ Image is formed on object side at 37.5 cm from pole of concave mirror.
(ii) The formula for the size of an image
Hi∕HO=−‌
v
u

Where Hi is the size of image.
Now,
‌
Hi
4‌cm
‌=‌
−(−37.5‌cm)
(−25‌cm)

Hi‌=‌
−4×37.5
25‌cm
=−6‌cm
∴ Image is formed on object side at 37.5 cm from pole of concave mirror.
(ii) The formula for the size of an image
Hi∕HO=−‌
v
u

Where Hi is the size of image.
Now,
‌
Hi
4‌cm
‌=‌
−(−37.5‌cm)
(−25‌cm)

Hi‌=‌
−4×37.5
25‌cm
=−6‌cm
∴ Size of image =6‌cm
Hence, screen should place 37.5‌cm left side of mirror and size of image is 6‌cm. It is inverted and larger than object's size.
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