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Write laws of refraction. Explain the same with the help of a ray diagram, when a ray of light passes through a rectangular glass slab.

Explanation:-

Laws of refraction: 

  1. The incident ray, the normal to any refracting surface at the point of incidence, and the refracted ray all lie in the same plane called the plane of incidence or plane of refraction.
  2. The ratio of the sine of the angle of incidence to the angle of refraction is always constant. 

                           \frac{\sin i}{\sin r}=\mathrm{constant}

                          

    \frac{\sin i}{\sin r}=\frac{\mu _{2}}{\mu _{1}}=\frac{v_{1}}{v_{2}}=\frac{\lambda_{1}}{\lambda_{2}}

or
     $$ \mu _{1} \sin i=\mu _{2} \sin r $$

\frac{\sin(i)}{ \sin(r)}= \mu _{21}     

= refractive index of the second medium with respect to the first medium.

For a glass slab as shown in the figure

i = angle of incidence

r1 = angle of reflection

\frac{sini}{sinr_1}=\frac{\mu_g}{\mu_{air}}

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Safeer PP

Two stones are thrown vertically upwards simultaneously with their initial velocities u1and u2 respectively. Prove that the heights reached by them would be in the ratio of u12 : u22 

(Assume upward acceleration is –g and downward acceleration to be +g ).

The height reached by any stone can be calculated by using the third equation of motion.

v^2=u^2+2as

We can use the fact, that at the highest point the velocity will be zero. The acceleration due to gravity will retard the particles.

Therefore, the height raised for any particle will be given as:

\\0^2=u^2+2as\\\Rightarrow h=\frac{u^2}{2g}

Therefore

\frac{h_1}{h_2}=\frac{u_1^2}{u_2^2}\\

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Safeer PP

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Obtain a relation for the distance traveled by an object moving with uniform acceleration in the interval between the 4th and 5th seconds.

Explanation:-

Distance travelled in nth second by any particle is equal to the difference of distances travelled in n seconds and n -1 seconds. For example. distance travelled in the fourth second is the difference between distance travel in four seconds and three seconds.

- Hence, by using the second equation of motion we can find out the distance travelled in nth second.

If the initial velocity is zero,

 In that case, the distance travelled in the fourth second and fifth second will be in the ratio of 7:9.

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Safeer PP

The barrel of a fountain pen, cylindrical in shape, is 7 cm long and 5 mm in diameter. A full barrel of ink in the pen is used upon writing 3300 words on average. How many words can be written in a bottle of ink containing one-fifth of a litre?

\\\text{Volume of the barrel}=\pi r^2h=\frac{22}{7}\times(0.25)^2\times7\\=1.375cm^3=\frac{1.375}{1000}L

3300 words can be written with 0.001375 L of ink

So with 1L of ink 3300/0.001375 words can be written=2400000

So with 1/5th of a litter 2400000/5 words can be written=48000

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rishi.raj

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How are the activities of the gastro-intestinal tract regulated?

Activities of digestive system regulate both Harmon and neural reflexes

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Pushpa Franshaw

In which plant will you look for mycorrhiza and coralloid roots? Also, explain what these terms mean.

Mycorrhiza, which is also known as ‘fungus-root’, is a mutually beneficial relationship between a plant root and a fungus. In most cases, the fungus grows within the roots of the plants and helps the plant to absorb water and nutrients, and in return, the plant provides the fungus with food, e.g., Pinus, a Gymnosperm.

Coralloid Roots: These roots are associated with nitrogen-fixing cyanobacteria. In coralloid roots, the nodules are formed in large numbers, giving the roots a coralloid appearance, e.g. Cycas and plants of Leguminosae.

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Safeer PP

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How are the male and female gametophytes of pteridophytes and gymnosperms different from each other?

The size of gametophyte of of pteridophytes quite large compare  to gymnosperm's gametophytes. Gametophyte of pteridophytes are photosynthetic in nature while gametophyte of  gymnosperms are are not photosynthetic in nature

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LOKESH JAIN

 Comment on the lifecycle and nature of a fern prothallus.

Pteridophytes show a haplo-diplontic life cycle.

Formation of spores:
The main plant body is a diploid sporophyte, which contains sporophylls. The plant can be homosporous, or it can be heterosporous, producing haploid smaller microspores and larger megaspores.

Germination:
Germination of spores produces haploid, free-living gametophytes called prothallus. The homosporous ferns give rise to bisexual gametophytes, and heterosporous ferns give rise to separate male and female gametophytes.

Formation of gametes:
The prothallus consists of a haploid male sex organ, antheridia and a female sex organ, archegonia, which give rise to antherozoids and eggs, respectively.

Fertilisation:
Fertilisation occurs with the help of water. The diploid zygote develops into an embryo that finally forms a sporophyte.

Nature of the prothallus:

Fern, which is a type of pteridophyte, reveals a haplo-diplontic state. It bears prothallus in the gametophytic stage. Prothallus is the free-living, multicellular, inconspicuous, haploid, photosynthetic, thalloid gametophyte of pteridophytes. It bears unicellular rhizoids for attachment to the substratum. The requirement for damp and moist places is due to the requirement of water for fertilization.

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Name the body part modified for food storage in the following 

(a) Carrot

(b) Colocasia

(c) Sweet potato

(d) Asparagus 

(e) Radish

(f) Potato

(g) Dahlia

(h) Turmeric

(i) Gladiolus

(j) Ginger

(k) Portulaca 

(a) Carrot- Tap Root

(b) Colocasia- Stem (corm)

(c) Sweet potato- Adventitious tuberous roots 

(d) Asparagus- Adventitious tuberous roots 

(e) Radish- Fusiform Roots

(f) Potato- Stem

(g) Dahlia- Adventitious tuberous roots

(h) Turmeric- Stem (Rhizome)

(i) Gladiolus- Stem (corm)

(j) Ginger- Stem

(k) Portulaca- Adventitious Roots

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Safeer PP

 Differentiate between

a. Bract and Bracteole

b. Pulvinus and petiole

c. Pedicel and peduncle

d. Spike and spadix

e. Stamen and staminoid

f. Pollen and pollinium

a. The bracteolate is a bract-like structure present at the base of the flower, while a bract is a leaf-like structure found towards the base of the pedicle.
b. Petiole is a subcylindrical stalk that connects the lamina with the leaf base, while Pulvinus is a swollen leaf base found in leguminous plants.
c. The Peduncle is the stalk of the whole inflorescence, while a pedicle is the stalk of a flower.
d. The spadix is covered by several large bracts known as spathes, while in a spike, sessile flowers are attached to an elongated peduncle.
e. Every stamen represents a male reproductive organ, and the androecium comprises stamens. Staminode is a sterile stamen. 
f. Polonium is defined as a group of pollen grains, while pollen is a male gametophyte of angiosperms.

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Safeer PP

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